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A247918 Expansion of (1 + x) / ((1 - x^4) * (1 + x^4 - x^5)) in powers of x. 3
1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 2, 0, -1, 2, -1, 2, 1, -2, 4, -3, 1, 4, -5, 7, -4, -2, 10, -12, 11, -1, -11, 22, -23, 13, 11, -33, 45, -35, 3, 44, -78, 81, -37, -41, 122, -158, 119, 4, -163, 281, -276, 115, 167, -443, 558, -391, -52, 611, -1000, 949 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,14

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,2,-2,2,-1).

FORMULA

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

0 = a(n) - a(n+1) - a(n+5) + mod(floor((n-1)/2),2) for all n in Z.

a(n) = -A247907(-8-n) for all n in Z.

Convolution of A077905 and A112553.

EXAMPLE

G.f. = 1 + x + x^5 + x^6 + x^8 + x^11 + 2*x^13 - x^15 + 2*x^16 - x^17 + ...

MATHEMATICA

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

PROG

(PARI) {a(n) = if( n<0, n=-8-n; polcoeff( -1 / ((1 - x) * (1 - x + x^2) * (1 + x^2) * (1 - x^2 - x^3)) + x * O(x^n), n), polcoeff( 1 / ((1 - x) * (1 - x + x^2) * (1 + x^2) * (1 + x - x^3)) + x * O(x^n), n))};

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

CROSSREFS

Cf. A077905, A112553, A247907

Sequence in context: A262436 A336499 A093998 * A237203 A339444 A029389

Adjacent sequences:  A247915 A247916 A247917 * A247919 A247920 A247921

KEYWORD

sign,easy

AUTHOR

Michael Somos, Sep 26 2014

STATUS

approved

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Last modified February 26 13:41 EST 2021. Contains 341632 sequences. (Running on oeis4.)