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

2,5

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.

Links

Table of n, a(n) for n=2..79.

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

Example

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,
...

Crossrefs

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

Sequence in context: A228125 A227588 A093628 * A114282 A112739 A308813

Adjacent sequences: A186804 A186805 A186806 * A186808 A186809 A186810

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 26 2011

Status

approved