

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



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.
Sequence in context: A179045 A106740 A178534 * A191861 A129761 A319299
Adjacent sequences: A110616 A110617 A110618 * A110620 A110621 A110622


KEYWORD

nonn,tabl


AUTHOR

Henry Bottomley, Aug 01 2005


STATUS

approved



