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A184642
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Number of partitions of n having no parts with multiplicity 7.
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8
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1, 1, 2, 3, 5, 7, 11, 14, 22, 29, 41, 54, 75, 97, 130, 168, 222, 283, 368, 465, 597, 750, 949, 1183, 1488, 1841, 2292, 2822, 3487, 4267, 5239, 6376, 7782, 9429, 11439, 13798, 16661, 20007, 24043, 28763, 34420, 41021, 48894, 58066, 68956, 81627, 96592
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: Product_{j>0} (1-x^(7*j)+x^(8*j))/(1-x^j).
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EXAMPLE
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a(7) = 14, because 14 partitions of 7 have no parts with multiplicity 7: [1,1,1,1,1,2], [1,1,1,2,2], [1,2,2,2], [1,1,1,1,3], [1,1,2,3], [2,2,3], [1,3,3], [1,1,1,4], [1,2,4], [3,4], [1,1,5], [2,5], [1,6], [7].
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, [0, 0],
add((l->`if`(j=7, [l[1]$2], l))(b(n-i*j, i-1)), j=0..n/i)))
end:
a:= n-> (l-> l[1]-l[2])(b(n, n)):
seq(a(n), n=0..50);
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, Sum[Function[l, If[j == 7, {l[[1]], l[[1]]}, l]][b[n - i*j, i - 1]], {j, 0, n/i}]]];
a[n_] := b[n, n][[1]] - b[n, n][[2]];
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CROSSREFS
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Cf. A000041, A183564, A183568, A007690, A116645, A118807, A184639, A184640, A184641, A184643, A184644, A184645.
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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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