A133683 Linear recurrence a(n) = a(n-3) + 2a(n-5), starting from all-one initial conditions.

1, 1, 1, 1, 1, 3, 3, 3, 5, 5, 9, 11, 11, 19, 21, 29, 41, 43, 67, 83, 101, 149, 169, 235, 315, 371, 533, 653, 841, 1163, 1395, 1907, 2469, 3077, 4233, 5259, 6891, 9171, 11413, 15357, 19689, 25195, 33699, 42515, 55909

Offset

1,6

Links

Table of n, a(n) for n=1..45.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 1, 0, 2).

Formula

O.g.f.: -x*(1+x+x^2)/(-1+x^3+2*x^5) . - R. J. Mathar, Jan 07 2008

Example

a(14) = a(11) + 2a(9) = 9 + 2*5 = 19

Mathematica

LinearRecurrence[{0, 0, 1, 0, 2}, {1, 1, 1, 1, 1}, 50] (* Harvey P. Dale, Jan 16 2012 *)

Prog

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 2, 0, 1, 0, 0]^(n-1)*[1; 1; 1; 1; 1])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016

Crossrefs

Sequence in context: A046702 A357057 A226592 * A182998 A117900 A318203

Adjacent sequences: A133680 A133681 A133682 * A133684 A133685 A133686

Keyword

easy,nonn

Author

David Eppstein, Jan 04 2008

Status

approved