A098528 Expansion of (1 + 2*x^3)/(1 - x - 4*x^7).

1, 1, 1, 3, 3, 3, 3, 7, 11, 15, 27, 39, 51, 63, 91, 135, 195, 303, 459, 663, 915, 1279, 1819, 2599, 3811, 5647, 8299, 11959, 17075, 24351, 34747, 49991, 72579, 105775, 153611, 221911, 319315, 458303, 658267, 948583, 1371683, 1986127, 2873771, 4151031

Offset

0,4

Comments

The expansion of (1 + k*x^2)/(1 - x - k^2*x^7) satisfies the recurrence a(n) = a(n-1) + k^2*a(n-7), a(0)=1, a(1)=1, a(2)=1, a(3)=k+1, a(4)=k+1, a(5)=k+1, a(6)=k+1 with a(n) = Sum_{k=0..floor(n/3)} binomial(n-3k, floor(k/2))*r^k.

Links

Table of n, a(n) for n=0..43.

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

Formula

a(n) = a(n-1) + 4*a(n-7);

a(n) = Sum_{k=0..floor(n/3)} binomial(n-3k, floor(k/2))*2^k.

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 0, 4}, {1, 1, 1, 3, 3, 3, 3}, 50] (* Harvey P. Dale, Jan 26 2014 *)

Prog

(PARI) Vec((1+2*x^3)/(1-x-4*x^7)+O(x^66)) \\ Joerg Arndt, Jan 28 2014

Crossrefs

Cf. A098524.

Sequence in context: A092531 A125002 A285245 * A242715 A078229 A222292

Adjacent sequences: A098525 A098526 A098527 * A098529 A098530 A098531

Keyword

easy,nonn

Author

Paul Barry, Sep 12 2004

Extensions

Name corrected by Harvey P. Dale, Jan 26 2014

Status

approved