A078436 Triangle read by rows in which n-th row counts multisets associated with hook partitions.

1, 2, 0, 3, 4, 0, 4, 6, 8, 0, 5, 8, 12, 16, 0, 6, 10, 16, 24, 32, 0, 7, 12, 20, 32, 48, 64, 0, 8, 14, 24, 40, 64, 96, 128, 0, 9, 16, 28, 48, 80, 128, 192, 256, 0, 10, 18, 32, 56, 96, 160, 256, 384, 512, 0, 11, 20, 36, 64, 112, 192, 320, 512, 768, 1024, 0, 12, 22, 40, 72, 128

Offset

1,2

Comments

Row sums appear to be A077802. When more general partition types are included, such as 22^(n-4) yielding 9 18 36 72 ..., the array row sums becomes 1,2,7,18,50,118,301,... in agreement with A074141.

Links

Table of n, a(n) for n=1..71.

Formula

G.f.: x*y*(2-x)/(1-2*x*y)/(1-x)^2. - Vladeta Jovovic, Dec 31 2002

Example

Triangle begins 1; 2,0; 3,4,0; 4,6,8,0; 5,8,12,16,0; ...
a(13) = 12 because we find 1 + 3 + 4 + 3 + 1 multisets of type 21^(n-2): they are 4; 14,24,34; 114,124,134,234; 1124,1134,1234; and 11234

Crossrefs

Cf. A077802, A074139, A074141.

Sequence in context: A102389 A099091 A227595 * A368090 A209705 A181289

Adjacent sequences: A078433 A078434 A078435 * A078437 A078438 A078439

Keyword

easy,nonn,tabl

Author

Alford Arnold, Dec 30 2002

Extensions

More terms from Vladeta Jovovic, Dec 31 2002

Status

approved