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A100133
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a(n) = Sum_{k=0..floor(n/4)} C(n-2k,2k) * 3^k * 2^(n-4k).
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4
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1, 2, 4, 8, 19, 50, 136, 368, 985, 2618, 6940, 18392, 48763, 129338, 343120, 910304, 2415025, 6406898, 16996852, 45090728, 119620579, 317340098, 841868632, 2233386320, 5924932489, 15718204970, 41698695820, 110622122360
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OFFSET
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0,2
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COMMENTS
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Binomial transform of 1,1,1,1,4,4,10,10,28,28,76,... (g.f. (1-x)(1+x)^2/(1-2x^2-2x^4)).
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LINKS
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FORMULA
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G.f.: (1-2x)/((1-2x)^2-3x^4).
a(n) = 4*a(n-1) - 4*a(n-2) + 3*a(n-4). [corrected by Kevin Ryde, Feb 02 2023]
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PROG
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(PARI) a(n) = sum(k=0, n\4, binomial(n-2*k, 2*k) * 3^k * 2^(n-4*k)); \\ Michel Marcus, Oct 09 2021
(PARI) my(p=Mod('x, 'x^4-4*'x^3+4*'x^2-3)); a(n) = subst(lift(p^n), 'x, 2); \\ Kevin Ryde, Feb 02 2023
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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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