A262593 Expansion of (1-3*x)^3/((1-x)^4*(1-4*x)).

1, -1, -3, -1, 13, 63, 237, 879, 3357, 13135, 52061, 207519, 829037, 3314719, 13256973, 53025423, 212098557, 848390319, 3393556477, 13574220095, 54296873421, 217187485439, 868749932077, 3474999717039, 13899998855133, 55599995405583, 222399981605277, 889599926401759, 3558399705585197

Offset

0,3

Comments

Suggested by A262592.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-22,28,-17,4).

Formula

a(n + 1) = (1/3)*(12*a(n) - 4*n^3 + 18*n^2 + 4*n - 15), a(0) = 1. - Ilya Gutkovskiy, Oct 22 2015

From Colin Barker, Oct 23 2015: (Start)

a(n) = 8*a(n-1)-22*a(n-2)+28*a(n-3)-17*a(n-4)+4*a(n-5) for n>4.

a(n) = (77+4^(1+n)-84*n-126*n^2+36*n^3)/81.

(End)

Prog

(PARI) Vec((1-3*x)^3/((1-x)^4*(1-4*x)) + O(x^40)) \\ Michel Marcus, Oct 23 2015
(PARI) a(n) = (77+4^(1+n)-84*n-126*n^2+36*n^3)/81 \\ Colin Barker, Oct 23 2015

Crossrefs

Cf. A262592.

Sequence in context: A008826 A103440 A116483 * A010290 A074960 A287740

Adjacent sequences: A262590 A262591 A262592 * A262594 A262595 A262596

Keyword

sign,easy

Author

N. J. A. Sloane, Oct 22 2015

Status

approved