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A054567
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a(n) = 4*n^2 - 7*n + 4.
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38
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1, 6, 19, 40, 69, 106, 151, 204, 265, 334, 411, 496, 589, 690, 799, 916, 1041, 1174, 1315, 1464, 1621, 1786, 1959, 2140, 2329, 2526, 2731, 2944, 3165, 3394, 3631, 3876, 4129, 4390, 4659, 4936, 5221, 5514, 5815, 6124, 6441, 6766, 7099, 7440, 7789, 8146
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OFFSET
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1,2
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COMMENTS
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The number 1 is placed in the middle of a sheet of squared paper and the numbers 2, 3, 4, 5, 6, etc. are written in a clockwise spiral around 1, as in A068225 etc. This sequence is read off along one of the rays from 1.
Ulam's spiral (W spoke of A054552). - Robert G. Wilson v, Oct 31 2011
Also, numbers of the form m*(4*m+1)+1 for nonnegative m. [Bruno Berselli, Jan 06 2016]
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LINKS
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Ivan Panchenko, Table of n, a(n) for n = 1..1000
Robert G. Wilson v, Cover of the March 1964 issue of Scientific American
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 8*n+a(n-1)-11 for n>1, a(1)=1. - Vincenzo Librandi, Aug 07 2010
a(n) = A204674(n-1) / n. [Reinhard Zumkeller, Jan 18 2012]
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: -x*(4*x^2+3*x+1) / (x-1)^3. - Colin Barker, Oct 25 2014
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MATHEMATICA
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Table[4 n^2 - 7 n + 4, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Sep 01 2008 *)
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PROG
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(PARI) Vec(-x*(4*x^2+3*x+1)/(x-1)^3 + O(x^100)) \\ Colin Barker, Oct 25 2014
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CROSSREFS
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Cf. A054566, A068225, A054552, A054554, A054556, A054569, A033951.
Cf. A266883: m*(4*m+1)+1 for m = 0,-1,1,-2,2,-3,3,...
Sequences on the four axes of the square spiral: Starting at 0: A001107, A033991, A007742, A033954; starting at 1: A054552, A054556, A054567, A033951.
Sequences on the four diagonals of the square spiral: Starting at 0: A002939 = 2*A000384, A016742 = 4*A000290, A002943 = 2*A014105, A033996 = 8*A000217; starting at 1: A054554, A053755, A054569, A016754.
Sequences obtained by reading alternate terms on the X and Y axes and the two main diagonals of the square spiral: Starting at 0: A035608, A156859, A002378 = 2*A000217, A137932 = 4*A002620; starting at 1: A317186, A267682, A002061, A080335.
Sequence in context: A354343 A106398 A179986 * A096957 A272811 A273206
Adjacent sequences: A054564 A054565 A054566 * A054568 A054569 A054570
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KEYWORD
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nonn,easy
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AUTHOR
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Enoch Haga, G. L. Honaker, Jr., Apr 10 2000
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EXTENSIONS
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Edited by Frank Ellermann, Feb 24 2002
Typo fixed by Charles R Greathouse IV, Oct 28 2009
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STATUS
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approved
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