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A184639
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Number of partitions of n having no parts with multiplicity 4.
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8
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1, 1, 2, 3, 4, 7, 10, 14, 19, 27, 37, 50, 67, 88, 115, 153, 196, 253, 324, 412, 524, 661, 828, 1036, 1290, 1603, 1980, 2443, 2997, 3671, 4487, 5460, 6631, 8034, 9703, 11703, 14075, 16890, 20226, 24175, 28838, 34332, 40801, 48394, 57307, 67765, 79974
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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) - A183561(n).
a(n) = A183568(n,0) - A183568(n,4).
G.f.: Product_{j>0} (1-x^(4*j)+x^(5*j))/(1-x^j).
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EXAMPLE
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a(4) = 4, because 4 partitions of 4 have no parts with multiplicity 4: [1,1,2], [2,2], [1,3], [4].
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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=4, [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 == 4, {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, A183561, A183568, A007690, A116645, A118807, A184640, A184641, A184642, A184643, A184644, A184645.
Sequence in context: A072958 A353837 A062426 * A035565 A240489 A056513
Adjacent sequences: A184636 A184637 A184638 * A184640 A184641 A184642
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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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