A110619 - OEIS

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A110619

Triangle of number of partitions of n with no part more than n/k; also partitions of n into n/k or fewer parts.

1, 2, 1, 3, 1, 1, 5, 3, 1, 1, 7, 3, 1, 1, 1, 11, 7, 4, 1, 1, 1, 15, 8, 4, 1, 1, 1, 1, 22, 15, 5, 5, 1, 1, 1, 1, 30, 18, 12, 5, 1, 1, 1, 1, 1, 42, 30, 14, 6, 6, 1, 1, 1, 1, 1, 56, 37, 16, 6, 6, 1, 1, 1, 1, 1, 1, 77, 58, 34, 19, 7, 7, 1, 1, 1, 1, 1, 1, 101, 71, 39, 21, 7, 7, 1, 1, 1, 1, 1, 1, 1, 135, 105

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..93.

FORMULA

T(n, k)=A008284(n+floor[n/k], floor[n/k]). T(0, k)=1; T(n, k)=0 for 0<n<k; T(n, k)=1 for k<=n<2k; T(n, 1)=A000041(n); T(n, 2)=A110618(n).

EXAMPLE

Rows start: 1; 2,1; 3,1,1; 5,3,1,1; 7,3,1,1,1; 11,7,4,1,1,1; etc.

T(7,3)=4 since 7 can be partitioned as 1+1+1+1+1+1+1, 2+1+1+1+1+1, 2+2+1+1+1, or 2+2+2+1 and also as 7, 6+1, 5+2, or 4+3.

CROSSREFS

First column is A000041, second is A110618.