A098526 Expansion of (1+4x^2)/(1-x-16x^5).

1, 1, 5, 5, 5, 21, 37, 117, 197, 277, 613, 1205, 3077, 6229, 10661, 20469, 39749, 88981, 188645, 359221, 686725, 1322709, 2746405, 5764725, 11512261, 22499861, 43663205, 87605685, 179841285, 364037461, 724035237, 1422646517, 2824337477

Offset

0,3

Comments

The expansion of (1+kx^2)/(1-x-k^2*x^5) satisfies the recurrence a(n)=a(n-1)+k^2*a(n-5),a(0)=1,a(1)=1,a(2)=k+1,a(3)=k+1,a(4)=k+1, with a(n)=sum{k=0..floor(n/2), binomial(n-2k,floor(k/2))r^k}.

Links

Harvey P. Dale, 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)+16a(n-5); a(n)=sum{k=0..floor(n/2), binomial(n-2k, floor(k/2))4^k}.

a(0)=1, a(1)=1, a(2)=5, a(3)=5, a(4)=5, a(n)=a(n-1)+16*a(n-5). - Harvey P. Dale, Jun 15 2014

Mathematica

CoefficientList[Series[(1+4x^2)/(1-x-16x^5), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 16}, {1, 1, 5, 5, 5}, 40] (* Harvey P. Dale, Jun 15 2014 *)

Crossrefs

Sequence in context: A260960 A283711 A365368 * A262122 A216876 A019162

Adjacent sequences: A098523 A098524 A098525 * A098527 A098528 A098529

Keyword

easy,nonn

Author

Paul Barry, Sep 12 2004

Status

approved