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A089076
Expansion of -x - x^3*(2 -2*x^4 +x^5)/((1-x^2)*(1+x+x^4)).
3
-1, 0, -2, 2, -4, 4, -6, 7, -11, 14, -20, 26, -37, 50, -70, 95, -132, 181, -251, 345, -477, 657, -908, 1252, -1729, 2385, -3293, 4544, -6273, 8657, -11950, 16493, -22766, 31422, -43372, 59864, -82630, 114051, -157423, 217286, -299916, 413966, -571389, 788674, -1088590, 1502555, -2073944, 2862617
OFFSET
1,3
FORMULA
G.f.: -x - x^3*(2 -2*x^4 +x^5)/((1-x^2)*(1+x+x^4)).
MATHEMATICA
Rest@CoefficientList[Series[-x -x^3*(2-2*x^4+x^5)/((1-x^2)*(1+x-x^4)), {x, 0, 50}], x] (* G. C. Greubel, Feb 19 2021 *)
LinearRecurrence[{-1, 1, 1, 1, 0, -1}, {-1, 0, -2, 2, -4, 4, -6, 7}, 50] (* Harvey P. Dale, Aug 11 2021 *)
PROG
(Sage)
def A089076_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( -x -x^3*(2-2*x^4+x^5)/((1-x^2)*(1+x-x^4)) ).list()
a=A089076_list(51); a[1:] # G. C. Greubel, Feb 19 2021
(Magma)
R<x>:=PowerSeriesRing(Integers(), 50);
Coefficients(R!( -x -x^3*(2-2*x^4+x^5)/((1-x^2)*(1+x-x^4)) )); // G. C. Greubel, Feb 19 2021
CROSSREFS
KEYWORD
sign
AUTHOR
Roger L. Bagula, Dec 04 2003
EXTENSIONS
Edited by G. C. Greubel, Feb 19 2021
STATUS
approved