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A084611
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a(n) = sum of absolute values of coefficients of (1+x-x^2)^n.
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6
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1, 3, 7, 13, 35, 83, 165, 367, 899, 1957, 3839, 9771, 22709, 43213, 102963, 255061, 525601, 1098339, 2798273, 6202969, 11746259, 29976073, 70898649, 140495779, 314391789, 787757461, 1688887719, 3337986541, 8583687613, 19647782463
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OFFSET
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0,2
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COMMENTS
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Limit_{n -> oo} a(n+1)/a(n) does not exist; however, lim_{n -> oo} a(n)^(1/n) = sqrt(5) (conjecture).
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LINKS
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MATHEMATICA
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Table[Sum[Abs[Coefficient[Expand[(1+x-x^2)^n], x, k]], {k, 0, 2*n}], {n, 0, 30}] (* Vaclav Kotesovec, Jul 28 2013 *)
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PROG
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(PARI) {a(n)=sum(k=0, 2*n, abs(polcoeff((1+x-x^2+x*O(x^k))^n, k)))}
for(n=0, 30, print1(a(n), ", "))
(Magma)
A084610:= func< n, k | (&+[Binomial(n, k-j)*Binomial(k-j, j)*(-1)^j: j in [0..k]]) >;
(SageMath)
def A084610(n, k): return sum(binomial(n, j)*binomial(n-j, k-2*j)*(-1)^j for j in range(k//2+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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