A233522 Expansion of 1 / (1 - x - x^4 + x^9) in powers of x.

1, 1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 16, 22, 29, 38, 50, 67, 89, 118, 156, 207, 274, 363, 481, 638, 845, 1119, 1482, 1964, 2602, 3447, 4566, 6049, 8013, 10615, 14062, 18629, 24678, 32691, 43306, 57369, 75998, 100676, 133367, 176674, 234043, 310041, 410717

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

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

Formula

a(n) = a(n-1) + a(n-4) - a(n-9) for all n in Z.

a(n) - a(n-1) = A017830(n).

G.f.: 1 / ((1 - x) * (1 + x) * (1 + x^2) * (1 - x - x^5)).

Example

G.f. = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 5*x^7 + 7*x^8 + ...

Mathematica

a[ n_] := SeriesCoefficient[ If[ n >= 0, 1 / (1 - x - x^4 + x^9), -x^9 / (1 - x^5 - x^8 + x^9)], {x, 0, Abs@n}];

Prog

(PARI) {a(n) = if( n>=0, polcoeff( 1 / (1 - x - x^4 + x^9) + x * O(x^n), n), polcoeff( -x^9 / (1 - x^5 - x^8 + x^9) + x * O(x^-n), -n))};
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/( 1-x-x^4+x^9))); // G. C. Greubel, Aug 08 2018

Crossrefs

Cf. A017830.

Sequence in context: A120149 A117597 A241336 * A112639 A375185 A290137

Adjacent sequences: A233519 A233520 A233521 * A233523 A233524 A233525

Keyword

nonn,easy

Author

Michael Somos, Dec 11 2013

Status

approved