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A089647 Number of triangular partitions of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A018129 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

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Last modified February 5 12:47 EST 2023. Contains 360084 sequences. (Running on oeis4.)