A186807 Triangle read by rows: T(n,p) (n >= 2, 1 <= p <= n-1) = number of compositions of n into p parts, with first part >= all other parts.

1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 4, 4, 3, 1, 1, 5, 7, 6, 3, 1, 1, 6, 11, 11, 8, 4, 1, 1, 7, 16, 19, 17, 11, 4, 1, 1, 8, 22, 31, 32, 26, 13, 5, 1, 1, 9, 29, 48, 56, 54, 35, 17, 5, 1, 1, 10, 37, 71, 93, 102, 82, 48, 20, 6, 1, 1, 11, 46, 101, 148, 180, 172, 120, 63, 24, 6, 1

Offset: 2

Author

N. J. A. Sloane, Feb 26 2011

Keywords

• nonn
• tabl

Comments

This triangle arose in connection with a problem involving "lunar arithmetic".

Take the triangle formed by the antidiagonals of A156041 and reverse each row.

Examples

			Triangle begins:
1,
1, 1,
1, 2, 1,
1, 3, 2, 1,
1, 4, 4, 3, 1,
1, 5, 7, 6, 3, 1,
1, 6, 11, 11, 8, 4, 1,
1, 7, 16, 19, 17, 11, 4, 1,
1, 8, 22, 31, 32, 26, 13, 5, 1,
1, 9, 29, 48, 56, 54, 35, 17, 5, 1,
...
		

Links

• D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
• Index entries for sequences related to dismal (or lunar) arithmetic

Crossrefs

Cf. A156041. This is also A184957 with the last diagonal omitted.