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A218512
Number of partitions of n in which any two parts differ by at most 10.
3
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 100, 133, 171, 223, 282, 362, 453, 572, 709, 884, 1084, 1337, 1626, 1984, 2394, 2896, 3468, 4162, 4951, 5897, 6972, 8249, 9696, 11402, 13330, 15586, 18131, 21090, 24417, 28264, 32580, 37541, 43097, 49449, 56544
OFFSET
0,3
LINKS
FORMULA
G.f.: 1 + Sum_{j>0} x^j / Product_{i=0..10} (1-x^(i+j)).
MAPLE
b:= proc(n, i, k) option remember; `if`(n<0 or k<0, 0,
`if`(n=0, 1, `if`(i<1, 0, b(n, i-1, k-1) +b(n-i, i, k))))
end:
a:= n-> `if`(n=0, 1, 0) +add(b(n-i, i, 10), i=1..n):
seq(a(n), n=0..80);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n < 0 || k < 0, 0, If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k - 1] + b[n - i, i, k]]]];
a[n_] := If[n == 0, 1, 0] + Sum[b[n - i, i, 10], {i, 1, n}];
Table[a[n], {n, 0, 80}] (* Jean-François Alcover, May 21 2018, translated from Maple *)
CROSSREFS
Column k=10 of A194621.
Sequence in context: A104501 A328546 A242697 * A008635 A008641 A341714
KEYWORD
nonn,changed
AUTHOR
Alois P. Heinz, Oct 31 2012
STATUS
approved