A073463 Triangle of number of partitions of 2n into powers of 2 where the largest part is 2^k.

1, 1, 1, 1, 2, 1, 1, 3, 2, 0, 1, 4, 4, 1, 0, 1, 5, 6, 2, 0, 0, 1, 6, 9, 4, 0, 0, 0, 1, 7, 12, 6, 0, 0, 0, 0, 1, 8, 16, 10, 1, 0, 0, 0, 0, 1, 9, 20, 14, 2, 0, 0, 0, 0, 0, 1, 10, 25, 20, 4, 0, 0, 0, 0, 0, 0, 1, 11, 30, 26, 6, 0, 0, 0, 0, 0, 0, 0, 1, 12, 36, 35, 10, 0, 0, 0, 0, 0, 0, 0, 0, 1, 13, 42, 44

Offset: 0

Author

Henry Bottomley, Aug 02 2002

Keywords

• easy
• nonn
• tabl

Comments

In the recurrence T(n,k)=T(n-1,k)+T([n/2],k-1): T(n-1,k) represents the partitions where the smallest part is 1 and T([n/2],k-1) those where it is not.

Examples

			Rows start:
  1;
  1, 1;
  1, 2, 1;
  1, 3, 2, 0;
  1, 4, 4, 1, 0;
  1, 5, 6, 2, 0, 0;
  ...
		

Links

• H. Bottomley, Illustration of initial terms

Crossrefs

Columns include A000012, A000027, A002620, A008804. Subsequent columns start like A000123 (offset). Row sums are A000123.

Formula

T(n, k) = T(n-1, k)+T([n/2], k-1) starting with T(n, 0)=1 and T(0, k)=0 for k>0.