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

Author

Michael Somos, Dec 11 2013

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

Cf. A017830.

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/( 1-x-x^4+x^9))); // G. C. Greubel, Aug 08 2018

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}];

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))};

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)).