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

Author

John W. Layman, Jan 02 2004

Keywords

• nonn
• nice

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.

Examples

			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..
		

Links

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

Crossrefs

Cf. A089299.

Extensions

More terms from Jon E. Schoenfield, Aug 06 2006