A247919 Expansion of 1 / (1 + x^4 - x^5) in powers of x.

1, 0, 0, 0, -1, 1, 0, 0, 1, -2, 1, 0, -1, 3, -3, 1, 1, -4, 6, -4, 0, 5, -10, 10, -4, -5, 15, -20, 14, 1, -20, 35, -34, 13, 21, -55, 69, -47, -8, 76, -124, 116, -39, -84, 200, -240, 155, 45, -284, 440, -395, 110, 329, -724, 835, -505, -219, 1053, -1559, 1340

Offset: 0

Author

Michael Somos, Sep 26 2014

Keywords

• sign
• easy

Examples

			G.f. = 1 - x^4 + x^5 + x^8 - 2*x^9 + x^10 - x^12 + 3*x^13 - 3*x^14 + x^15 + ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,-1,1).

Crossrefs

Cf. A003520, A010892, A247917.

Programs

Magma

m:=60; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1 + x^4 - x^5)));  // G. C. Greubel, Aug 04 2018

Mathematica

CoefficientList[Series[1/(1 + x^4 - x^5), {x, 0, 100}], x] (* Vincenzo Librandi, Sep 27 2014 *)
LinearRecurrence[{0,0,0,-1,1},{1,0,0,0,-1},60] (* Harvey P. Dale, Sep 11 2024 *)

PARI

{a(n) = if( n<0, n=-5-n; polcoeff( 1 / (1 - x - x^5) + x * O(x^n), n), polcoeff( 1 / (1 + x^4 - x^5) + x * O(x^n), n))};

Formula

G.f.: 1 / ((1 - x + x^2) * (1 + x - x^3)).

Convolution of A010892 and A247917.

a(-5-n) = A003520(n) for all n in Z.

0 = a(n) - a(n+1) - a(n+5) for all n in Z.