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A220753
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Expansion of (1+4*x+5*x^2-x^3)/((1-x)*(1+x)*(1-2*x^2)).
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0
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1, 4, 8, 11, 22, 25, 50, 53, 106, 109, 218, 221, 442, 445, 890, 893, 1786, 1789, 3578, 3581, 7162, 7165, 14330, 14333, 28666, 28669, 57338, 57341, 114682, 114685, 229370, 229373, 458746, 458749, 917498, 917501, 1835002, 1835005, 3670010, 3670013
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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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G.f.: (1+4*x+5*x^2-x^3)/((1-x)*(1+x)*(1-2*x^2)).
a(n) = a(n-1)*2 if n even.
a(n) = a(n-1)+3 if n odd.
a(n) = 3*a(n-2) - 2*a(n-4) with a(0)=1, a(1)=4, a(2)=8, a(3)=11.
a(n) = 7*2^floor(n/2) - (3/2)*(3+(-1)^n).
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MATHEMATICA
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Table[7 2^Floor[n/2] - (3/2) (3 + (-1)^n), {n, 0, 40}] (* Bruno Berselli, Apr 13 2013 *)
LinearRecurrence[{0, 3, 0, -2}, {1, 4, 8, 11}, 40] (* T. D. Noe, Apr 17 2013 *)
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PROG
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(Magma) m:=41; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+4*x+5*x^2-x^3)/((1-x)*(1+x)*(1-2*x^2)))); // Bruno Berselli, Apr 13 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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