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A107443 Expansion of g.f.: (1+3*x^2)/((1-x)*(1+x+2*x^2)*(1-x+2*x^2)). 2
1, 1, 1, 1, -3, -3, 9, 9, -11, -11, 1, 1, 45, 45, -135, -135, 229, 229, -143, -143, -483, -483, 2025, 2025, -4139, -4139, 4321, 4321, 3597, 3597, -28071, -28071, 69829, 69829, -97199, -97199, 12285, 12285, 351945, 351945, -1104971, -1104971, 1907137, 1907137, -1301523, -1301523, -3723975, -3723975 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
a(2n) = a(2n+1) = A174565(n).
a(n) = (1 - 2*(-1)^n*A001607(n) + A001607(n+1))/2. - G. C. Greubel, Mar 24 2024
MAPLE
with(gfun): seriestolist(series((3*x^2+1)/((1-x)*(2*x^2+x+1)*(2*x^2-x+1)), x=0, 50));
MATHEMATICA
CoefficientList[Series[(1+3*x^2)/((1-x)*(1+3*x^2+4*x^4)), {x, 0, 50}], x] (* G. C. Greubel, Mar 24 2024 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+3*x^2)/((1-x)*(1+3*x^2+4*x^4)) )); // G. C. Greubel, Mar 24 2024
(SageMath)
def A107443_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+3*x^2)/((1-x)*(1+3*x^2+4*x^4)) ).list()
A107443_list(50) # G. C. Greubel, Mar 24 2024
CROSSREFS
Sequence in context: A064235 A098355 A183429 * A204099 A062234 A168329
KEYWORD
easy,sign
AUTHOR
Creighton Dement, May 26 2005
STATUS
approved

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Last modified May 19 00:35 EDT 2024. Contains 372666 sequences. (Running on oeis4.)