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A008464
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a(n) = 2^(2n+3) - 2^n*(n+3).
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6
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1, 5, 24, 108, 464, 1936, 7936, 32192, 129792, 521472, 2091008, 8375296, 33525760, 134156288, 536739840, 2147205120, 8589344768, 34358493184, 137436332032, 549750308864, 2199011721216, 8796068904960, 35184321757184, 140737383497728, 562949735317504
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OFFSET
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-1,2
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COMMENTS
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a(n-2) = 2^(2n-1) - (n+1)*2^(n-2) is number of compositions of 2n where each part <= n: e.g., for n=2, 4 can be written 5 ways with no part greater than 2 as 1+1+1+1 = 1+1+2 = 1+2+1 = 2+1+1 = 2+2. - Henry Bottomley, Feb 03 2003
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LINKS
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FORMULA
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G.f.: 8/(1-4*x) - 3/(1-2*x) - 2*x/(1-2*x)^2 + 1/x. - R. J. Mathar, Nov 21 2007
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MAPLE
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MATHEMATICA
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Table[Coefficient[Series[(1 - x)/(1 - 2 x + x^(n + 1)), {x, 0, 2 n}], x^(2 n)], {n, 1, 22}] (* Geoffrey Critzer, May 29 2013 *)
LinearRecurrence[{8, -20, 16}, {1, 5, 24}, 30] (* Harvey P. Dale, May 15 2022 *)
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PROG
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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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