A089647 Number of triangular partitions of n.

1, 1, 1, 2, 2, 4, 6, 8, 12, 18, 26, 37, 54, 76, 111, 156, 221, 310, 438, 608, 850, 1178, 1633, 2251, 3104, 4257, 5837, 7972, 10866, 14772, 20042, 27121, 36625, 49356, 66366, 89077, 119319, 159547, 212942, 283753, 377423, 501274, 664639, 879963

Offset

0,4

Comments

Number of ways of writing n as a sum [p(1,1) + p(1,2) + ... + p(1,k)] + [p(2,1) + ... + p(2,k-1)] + [p(3,1) + ... + p(3,k-2)] + ... + [p(k,1)] for some k =0, 1, 2, ..., so that in the triangular array {p(i,j)} the numbers are nonincreasing along rows and columns. All the p(i,j) are >= 1.

Links

Jon E. Schoenfield, Table of n, a(n) for n = 0..64

Example

a(8)=12, as seen from the following list:
8...61..51..41..52..42..32..43..33..311.211.221
....1...2...3...1...2...3...1...2...11..21..11.
....................................1...1...1..

Crossrefs

Cf. A089299.

Sequence in context: A361298 A091915 A123862 * A274152 A274155 A145465

Adjacent sequences: A089644 A089645 A089646 * A089648 A089649 A089650

Keyword

nonn,nice

Author

John W. Layman, Jan 02 2004

Extensions

More terms from Jon E. Schoenfield, Aug 06 2006

Status

approved