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A184641
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Number of partitions of n having no parts with multiplicity 6.
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8
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1, 1, 2, 3, 5, 7, 10, 15, 21, 29, 40, 54, 72, 96, 127, 166, 216, 279, 358, 457, 580, 735, 924, 1159, 1446, 1799, 2228, 2752, 3388, 4158, 5087, 6207, 7551, 9165, 11093, 13401, 16144, 19412, 23286, 27882, 33310, 39727, 47289, 56191, 66647, 78923, 93299
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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^(6*j)+x^(7*j))/(1-x^j).
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EXAMPLE
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a(6) = 10, because 10 partitions of 6 have no parts with multiplicity 6: [1,1,1,1,2], [1,1,2,2], [2,2,2], [1,1,1,3], [1,2,3], [3,3], [1,1,4], [2,4], [1,5], [6].
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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=6, [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 == 6, {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, A183563, A183568, A007690, A116645, A118807, A184639, A184640, A184642, 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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