A098582 Expansion of (1+2*x+4*x^2+8*x^3)/(1-x-16*x^5).

1, 3, 7, 15, 15, 31, 79, 191, 431, 671, 1167, 2431, 5487, 12383, 23119, 41791, 80687, 168479, 366607, 736511, 1405167, 2696159, 5391823, 11257535, 23041711, 45524383, 88662927, 174932095, 355052655, 723720031, 1452110159, 2870716991

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,16).

Formula

a(n) = a(n-1) + 16*a(n-5).

a(n) = Sum_{k=0..n} binomial(n-k, floor(k/4)) * 2^k.

Mathematica

CoefficientList[Series[(1+2*x+4*x^2+8*x^3)/(1-x-16*x^5), {x, 0, 50}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 16}, {1, 3, 7, 15, 15}, 50] (* G. C. Greubel, Feb 03 2018 *)

Prog

(PARI) x='x+O('x^30); Vec((1+2*x+4*x^2+8*x^3)/(1-x-16*x^5)) \\ G. C. Greubel, Feb 03 2018
(Magma) I:=[1, 3, 7, 15, 15]; [n le 5 select I[n] else Self(n-1) +16*Self(n-5): n in [1..30]]; // G. C. Greubel, Feb 03 2018

Crossrefs

Sequence in context: A117589 A295930 A143703 * A235698 A089432 A111294

Adjacent sequences: A098579 A098580 A098581 * A098583 A098584 A098585

Keyword

easy,nonn

Author

Paul Barry, Sep 16 2004

Status

approved