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A097081
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a(n) = Sum_{k=0..n} C(n,4k)*2^k.
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0
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1, 1, 1, 1, 3, 11, 31, 71, 145, 289, 601, 1321, 2979, 6683, 14743, 32111, 69697, 151777, 332113, 728689, 1598883, 3503627, 7668079, 16774775, 36704017, 80343361, 175916521, 385196761, 843365379, 1846290395, 4041672871, 8847607391
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OFFSET
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0,5
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LINKS
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FORMULA
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G.f.: (1-x)^3/((1-x)^4-2*x^4);
a(n) = Sum_{k=0..floor(n/2)} binomial(n,4*k)*2^k;
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)+a(n-4).
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MATHEMATICA
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Table[Sum[Binomial[n, 4k]2^k, {k, 0, n}], {n, 0, 40}] (* or *) LinearRecurrence[ {4, -6, 4, 1}, {1, 1, 1, 1}, 40] (* Harvey P. Dale, Feb 26 2012 *)
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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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STATUS
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approved
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