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A097073
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Expansion of (1-x+2*x^2)/((1+x)*(1-2*x)).
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25
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1, 0, 4, 4, 12, 20, 44, 84, 172, 340, 684, 1364, 2732, 5460, 10924, 21844, 43692, 87380, 174764, 349524, 699052, 1398100, 2796204, 5592404, 11184812, 22369620, 44739244, 89478484, 178956972, 357913940, 715827884, 1431655764, 2863311532
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OFFSET
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0,3
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COMMENTS
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Pairwise sums are {1, 1, 4, 16, 32, ...} or 2^n -Sum_{k=0..n} binomial(n,k)*(-1)^(n+k)*k.
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LINKS
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FORMULA
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a(n) = (2*2^n + 4*(-1)^n)/3 - 0^n.
a(n) = A001045(n+1) + (-1)^n - 0^n.
G.f.: 1 - x + x*Q(0), where Q(k) = 1 + 2*x^2 + (4*k+5)*x - x*(4*k+1 + 2*x)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 07 2013
E.g.f.: (1/3)*( 2*exp(2*x) + 4*exp(-x) - 3 ). - G. C. Greubel, Aug 19 2022
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MATHEMATICA
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CoefficientList[Series[(1-x+2x^2)/((1+x)(1-2x)), {x, 0, 40}], x] (* Harvey P. Dale, Dec 10 2012 *)
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PROG
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(SageMath)
def A097073(n): return 1 if (n==0) else 2*(2^n +2*(-1)^n)/3
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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Obscure variable k in Orlovsky comment replaced with a(n) by R. J. Mathar, Apr 23 2009
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STATUS
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approved
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