A379277 Number of solid partitions with multiplicities of parts matching the n-th composition in standard order.

1, 3, 3, 6, 9, 6, 9, 13, 21, 24, 33, 13, 21, 24, 33, 24, 48, 57, 84, 51, 93, 90, 135, 24, 48, 57, 84, 51, 93, 90, 135, 48, 102, 144, 213, 138, 258, 252, 387, 111, 228, 282, 426, 219, 417, 408, 633, 48, 102, 144, 213, 138, 258, 252, 387, 111, 228, 282, 426, 219

Offset

1,2

Links

John Tyler Rascoe, Table of n, a(n) for n = 1..1024

John Tyler Rascoe, Python program.

Formula

a(2^k) = A000219(k+1).

a(2^k-1) = A207542(k) for k > 0.

Example

The 5th composition in standard order, (2,1) corresponds to a solid partition with 3 parts (a,b,c) with a = b and a > c. There are 9 ways to arrange these parts into valid a solid partition giving a(5) = 9.

Prog

(Python) # see links

Crossrefs

Cf. A000041, A000219, A000293, A066099, A207542.

Sequence in context: A205970 A104715 A164743 * A110769 A093445 A098358

Adjacent sequences: A379274 A379275 A379276 * A379278 A379279 A379280

Keyword

nonn

Author

John Tyler Rascoe, Dec 19 2024

Status

approved