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A059722
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a(n) = n*(2*n^2 - 2*n + 1).
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11
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0, 1, 10, 39, 100, 205, 366, 595, 904, 1305, 1810, 2431, 3180, 4069, 5110, 6315, 7696, 9265, 11034, 13015, 15220, 17661, 20350, 23299, 26520, 30025, 33826, 37935, 42364, 47125, 52230, 57691, 63520, 69729, 76330, 83335, 90756, 98605, 106894, 115635, 124840
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OFFSET
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0,3
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COMMENTS
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Mean of the first four nonnegative powers of 2n+1, i.e., ((2n+1)^0 + (2n+1)^1 + (2n+1)^2 + (2n+1)^3)/4. E.g., a(2) = (1 + 3 + 9 + 27)/4 = 10.
Equatorial structured meta-diamond numbers, the n-th number from an equatorial structured n-gonal diamond number sequence. There are no 1- or 2-gonal diamonds, so 1 and (n+2) are used as the first and second terms since all the sequences begin as such. - James A. Record (james.record(AT)gmail.com), Nov 07 2004
Starting with offset 1 = row sums of triangle A143803. - Gary W. Adamson, Sep 01 2008
Form an array from the antidiagonals containing the terms in A002061 to give antidiagonals 1; 3,3; 7,4,7; 13,8,8,13; 21,14,9,14,21; and so on. The difference between the sum of the terms in n+1 X n+1 matrices and those in n X n matrices is a(n) for n>0. - J. M. Bergot, Jul 08 2013
Sum of the numbers from (n-1)^2 to n^2. - Wesley Ivan Hurt, Sep 08 2014
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n) = A053698(2*n-1)/4.
a(n) = sum(j=1..n, (n+j-1)^2-j^2+1 ). - Zerinvary Lajos, Sep 13 2006
G.f.: x*(1+x)*(1+5*x)/(1-x)^4. a(n)= A002414(n-1)+A002414(n). a(n+1)-a(n) = A136392(n+1). - R. J. Mathar, Sep 02 2008
a(n) = (A000290(n) + A000290(n+1)) * (A000217(n+1) - A000217(n)). - J. M. Bergot, Nov 02 2012
a(n) = n * A001844(n-1). - Doug Bell, Aug 18 2015
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MAPLE
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A059722:=n->n*(2*n^2 - 2*n + 1): seq(A059722(n), n=0..50); # Wesley Ivan Hurt, Sep 08 2014
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MATHEMATICA
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Table[n (2 n^2 - 2 n + 1), {n, 0, 50}] (* Wesley Ivan Hurt, Sep 08 2014 *)
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PROG
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(PARI) { for (n=0, 1000, write("b059722.txt", n, " ", n*(2*n^2 - 2*n + 1)); ) } \\ Harry J. Smith, Jun 28 2009
(MAGMA) [n*(2*n^2 - 2*n + 1) : n in [0..50]]; // Wesley Ivan Hurt, Sep 08 2014
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CROSSREFS
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Cf. A000330, A005900, A081436, A100178, A100179, A059722: "equatorial" structured diamonds; A000447: "polar" structured meta-diamond; A006484 for other structured meta numbers; and A100145 for more on structured numbers. - James A. Record (james.record(AT)gmail.com), Nov 07 2004
Cf. A059721, A059723.
Cf. A143803.
Sequence in context: A156674 A022277 A188480 * A229325 A074225 A055514
Adjacent sequences: A059719 A059720 A059721 * A059723 A059724 A059725
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KEYWORD
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nonn,easy
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AUTHOR
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Henry Bottomley, Feb 07 2001
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EXTENSIONS
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Edited with new definition by N. J. A. Sloane, Aug 29 2008
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STATUS
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approved
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