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A084775
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a(n) = sum of absolute valued coefficients of (1+x-4*x^2)^n.
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8
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1, 6, 34, 184, 956, 4776, 22986, 118304, 624634, 3281346, 17687330, 92606914, 470392898, 2348031430, 11932314170, 62345998488, 326780375778, 1691296908076, 8780141027670, 45168987187058, 230213109996786
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..2*n} abs(f(n, k)), where f(n, k) = ((sqrt(17) -1)/2)^k * Sum_{j=0..k} binomial(n, j)*binomial(n, k-j)*(-1)^j*((1+sqrt(17))/4 )^(2*j). - G. C. Greubel, Jun 03 2023
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MATHEMATICA
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T[n_, k_]:=T[n, k]=SeriesCoefficient[Series[(1+x-2*x^2)^n, {x, 0, 2n}], k];
a[n_]:= a[n]= Sum[Abs[T[[k+1]]], {k, 0, 2n}];
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PROG
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(PARI) for(n=0, 40, S=sum(k=0, 2*n, abs(polcoeff((1+1*x-4*x^2)^n, k, x))); print1(S", "))
(Magma)
R<x>:=PowerSeriesRing(Integers(), 100);
f:= func< n, k | Coefficient(R!( (1+x-4*x^2)^n ), k) >;
[(&+[ Abs(f(n, k)): k in [0..2*n]]): n in [0..40]]; // G. C. Greubel, Jun 03 2023
(SageMath)
def f(n, k):
P.<x> = PowerSeriesRing(QQ)
return P( (1+x-4*x^2)^n ).list()[k]
def a(n): return sum( abs(f(n, k)) for k in range(2*n+1) )
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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