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A247919 Expansion of 1 / (1 + x^4 - x^5) in powers of x. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

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).

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.

EXAMPLE

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

MATHEMATICA

CoefficientList[Series[1/(1 + x^4 - x^5), {x, 0, 100}], x] (* Vincenzo Librandi, Sep 27 2014 *)

PROG

(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))};

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

CROSSREFS

Cf. A003520, A010892, A247917.

Sequence in context: A321918 A321754 A321752 * A127839 A017827 A279778

Adjacent sequences:  A247916 A247917 A247918 * A247920 A247921 A247922

KEYWORD

sign,easy

AUTHOR

Michael Somos, Sep 26 2014

STATUS

approved

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Last modified February 26 14:18 EST 2021. Contains 341632 sequences. (Running on oeis4.)