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

0,4

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).

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.

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 *)

Prog

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

Crossrefs

Cf. A015445.

Sequence in context: A344336 A168416 A141324 * A331057 A205724 A040091

Adjacent sequences: A097038 A097039 A097040 * A097042 A097043 A097044

Keyword

easy,nonn

Author

Paul Barry, Jul 20 2004

Status

approved