A098525 Expansion of (1+3x^2)/(1-x-9x^5).

1, 1, 4, 4, 4, 13, 22, 58, 94, 130, 247, 445, 967, 1813, 2983, 5206, 9211, 17914, 34231, 61078, 107932, 190831, 352057, 660136, 1209838, 2181226, 3898705, 7067218, 13008442, 23896984, 43528018, 78616363, 142221325, 259297303, 474370159

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 (1,0,0,0,9).

Formula

a(n)=a(n-1)+9a(n-5); a(n)=sum{k=0..floor(n/2), binomial(n-2k, floor(k/2))3^k}.

Mathematica

CoefficientList[Series[(1+3x^2)/(1-x-9x^5), {x, 0, 50}], x] (* or *) LinearRecurrence[ {1, 0, 0, 0, 9}, {1, 1, 4, 4, 4}, 50] (* Harvey P. Dale, Oct 10 2019 *)

Crossrefs

Sequence in context: A261321 A245517 A179526 * A141666 A102127 A201625

Adjacent sequences: A098522 A098523 A098524 * A098526 A098527 A098528

Keyword

easy,nonn

Author

Paul Barry, Sep 12 2004

Status

approved