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A244239
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Number of partitions of n into 3 parts such that every i-th smallest part (counted with multiplicity) is different from i.
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3
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1, 3, 4, 6, 7, 9, 11, 13, 15, 18, 20, 23, 26, 29, 32, 36, 39, 43, 47, 51, 55, 60, 64, 69, 74, 79, 84, 90, 95, 101, 107, 113, 119, 126, 132, 139, 146, 153, 160, 168, 175, 183, 191, 199, 207, 216, 224, 233, 242, 251, 260, 270, 279, 289, 299, 309, 319, 330, 340
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OFFSET
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9,2
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6) for n > 15.
G.f.: x^9*(-x^6 + 2*x^4 + x^3 - 2*x - 1)/((x - 1)^3*(x + 1)*(x^2 + x + 1)). (End)
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MAPLE
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a:= proc(n) option remember; `if`(n<14, [1, 3, 4, 6, 7][n-8],
((-4*n+56)*a(n-5) +(3*n-16)*a(n-4) +(7*n-66)*a(n-3)
+(4*n-44)*a(n-2) +(28-3*n)*a(n-1)) / (7*n-78))
end:
seq(a(n), n=9..80);
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, Function[p, Expand[x*(p-Coefficient[p, x, i-1]*x^(i-1))]][b[n-i, i]]]]];
a[n_] := Coefficient[b[n, n], x, 3];
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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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