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A081435
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Diagonal in array of n-gonal numbers A081422.
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9
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1, 5, 18, 46, 95, 171, 280, 428, 621, 865, 1166, 1530, 1963, 2471, 3060, 3736, 4505, 5373, 6346, 7430, 8631, 9955, 11408, 12996, 14725, 16601, 18630, 20818, 23171, 25695, 28396, 31280, 34353, 37621, 41090, 44766, 48655, 52763, 57096, 61660
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OFFSET
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0,2
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COMMENTS
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One of a family of sequences with palindromic generators.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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a(n) = (2*n^3 +3*n^2 +3*n +2)/2.
G.f.: (1 +3*x^2 -4*x^3)/(1-x)^5.
E.g.f.: (2 +8*x +9*x^2 +2*x^3)*exp(x)/2. - G. C. Greubel, Aug 14 2019
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MAPLE
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a := n-> (n+1)*(2*(n+1)^2-3*n)/2; seq(a(n), n = 0..40); # G. C. Greubel, Aug 14 2019
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MATHEMATICA
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Table[(n^3 +(n+1)^3 -1)/2 +1, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, May 04 2011 *)
CoefficientList[Series[(1 +3x^2 -4x^3)/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 08 2013 *)
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PROG
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(Magma) [(2*n^3+3*n^2+3*n+2)/2: n in [0..40]]; // Vincenzo Librandi, Aug 08 2013
(PARI) vector(40, n, n--; (n+1)*(2*(n+1)^2-3*n)/2) \\ G. C. Greubel, Aug 14 2019
(Sage) [(n+1)*(2*(n+1)^2-3*n)/2 for n in (0..40)] # G. C. Greubel, Aug 14 2019
(GAP) List([0..40], n-> (n+1)*(2*(n+1)^2-3*n)/2); # G. C. Greubel, Aug 14 2019
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CROSSREFS
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Cf. A081434, A081436, A081437.
Sequence in context: A270944 A272457 A340974 * A272748 A273559 A272792
Adjacent sequences: A081432 A081433 A081434 * A081436 A081437 A081438
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Barry, Mar 21 2003
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STATUS
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approved
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