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A184645
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Number of partitions of n having no parts with multiplicity 10.
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8
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1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 56, 76, 100, 133, 174, 227, 293, 378, 482, 614, 777, 980, 1229, 1538, 1913, 2375, 2936, 3619, 4445, 5447, 6650, 8102, 9844, 11929, 14421, 17397, 20934, 25141, 30130, 36035, 43014, 51253, 60952, 72367, 85771, 101488
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n) = A000041(n) - A183567(n).
a(n) = A183568(n,0) - A183568(n,10).
G.f.: Product_{j>0} (1-x^(10*j)+x^(11*j))/(1-x^j).
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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=10, [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 == 10, {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]];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Apr 30 2018, after Alois P. Heinz *)
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CROSSREFS
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Cf. A000041, A183567, A183568, A007690, A116645, A118807, A184639, A184640, A184641, A184642, A184643, A184644.
Sequence in context: A036009 A261776 A027344 * A053691 A242696 A218510
Adjacent sequences: A184642 A184643 A184644 * A184646 A184647 A184648
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Jan 18 2011
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STATUS
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approved
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