A098524 Expansion of (1+2x^2)/(1-x-4x^5).

1, 1, 3, 3, 3, 7, 11, 23, 35, 47, 75, 119, 211, 351, 539, 839, 1315, 2159, 3563, 5719, 9075, 14335, 22971, 37223, 60099, 96399, 153739, 245623, 394515, 634911, 1020507, 1635463, 2617955, 4196015, 6735659, 10817687, 17359539, 27831359, 44615419

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

Table of n, a(n) for n=0..38.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,4).

Formula

a(n)=a(n-1)+4a(n-5); a(n)=sum{k=0..floor(n/2), binomial(n-2k, floor(k/2))2^k}.

Mathematica

CoefficientList[Series[(1+2x^2)/(1-x-4x^5), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 4}, {1, 1, 3, 3, 3}, 50] (* Harvey P. Dale, Mar 02 2024 *)

Crossrefs

Sequence in context: A200076 A342335 A137438 * A143015 A295671 A107709

Adjacent sequences: A098521 A098522 A098523 * A098525 A098526 A098527

Keyword

easy,nonn

Author

Paul Barry, Sep 12 2004

Status

approved