A064096 Fifth diagonal of triangle A064094.

1, 14, 67, 190, 413, 766, 1279, 1982, 2905, 4078, 5531, 7294, 9397, 11870, 14743, 18046, 21809, 26062, 30835, 36158, 42061, 48574, 55727, 63550, 72073, 81326, 91339, 102142, 113765, 126238, 139591, 153854, 169057, 185230, 202403, 220606, 239869, 260222, 281695, 304318, 328121, 353134, 379387, 406910

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 1+3*n+5*n^2+5*n^3. Fourth row polynomial (n=3) of Catalan triangle A009766.

G.f.: (1+2*x)*(1+8*x+x^2)/(1-x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Nov 17 2022

E.g.f.: (1 + 13*x + 20*x^2 + 5*x^3)*exp(x). - G. C. Greubel, Nov 07 2024

Mathematica

CoefficientList[Series[(1 + 2*x)*(1 + 8*x + x^2)/(1 - x)^4, {x, 0, 50}], x] (* Wesley Ivan Hurt, Nov 17 2022 *)

Prog

(Magma) [(n+1)^3 +2*n^2*(2*n+1): n in [0..50]]; // G. C. Greubel, Nov 07 2024
(SageMath)
def A064096(n): return (n+1)^3 +2*n^2*(2*n+1)
[A064096(n) for n in range(51)] # G. C. Greubel, Nov 07 2024

Crossrefs

Cf. A001844 (fourth diagonal), A009766, A064094.

Sequence in context: A249291 A280401 A221703 * A250141 A071616 A008529

Adjacent sequences: A064093 A064094 A064095 * A064097 A064098 A064099

Keyword

nonn,easy

Author

Wolfdieter Lang, Sep 13 2001

Extensions

More terms added by G. C. Greubel, Nov 07 2024

Status

approved