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A027196
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Number of partitions of n into an even number of parts, the least being 4; also, a(n+4) = number of partitions of n into an odd number of parts, each >=4.
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2
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0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 12, 14, 17, 20, 25, 29, 35, 41, 50, 58, 70, 81, 97, 113, 134, 156, 185, 214, 252, 292, 343, 396, 463, 534, 623, 718, 833, 958, 1110, 1274, 1471, 1686, 1943, 2223, 2555, 2919, 3347, 3818, 4368
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OFFSET
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1,16
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LINKS
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FORMULA
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G.f.: x^8 * Sum_{k>=0} x^(8*k)/Product_{j=1..2*k+1} (1-x^j). - Seiichi Manyama, May 15 2023
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MAPLE
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b:= proc(n, i, t) option remember; `if`(n=0, t,
`if`(i>n, 0, b(n, i+1, t)+b(n-i, i, 1-t)))
end:
a:= n-> `if`(n<4, 0, b(n-4, 4, 0)):
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MATHEMATICA
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b[n_, i_, t_] := b[n, i, t] = If[n == 0, t, If[i > n, 0, b[n, i + 1, t] + b[n - i, i, 1 - t]]];
a[n_] := If[n < 4, 0, b[n - 4, 4, 0]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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