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

Offset

0,2

Links

Table of n, a(n) for n=0..30.

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

Mathematica

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

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

Status

approved