A097041 Expansion of (1+x)/(1-x^2-9*x^3).

1, 1, 1, 10, 10, 19, 100, 109, 271, 1009, 1252, 3448, 10333, 14716, 41365, 107713, 173809, 479998, 1143226, 2044279, 5463208, 12333313, 23861719, 61502185, 134861536, 276257656, 688381201, 1490011480, 3174700105, 7685442289

Offset: 0

Author

Paul Barry, Jul 20 2004

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1,9).

Crossrefs

Cf. A015445.

Programs

Mathematica

CoefficientList[Series[(1+x)/(1-x^2-9x^3),{x,0,30}],x] (* or *) LinearRecurrence[{0,1,9},{1,1,1},30] (* Harvey P. Dale, Mar 12 2015 *)

PARI

x='x+O('x^50); Vec((1+x)/(1-x^2-9*x^3)) \\ G. C. Greubel, Apr 30 2017

Formula

a(n) = a(n-2) + 9*a(n-3).

a(n) = Sum_{k=0..floor(n/2)} binomial(floor((n-k)/2), k)*9^k.