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

Author

John Tyler Rascoe, Dec 19 2024

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Python

# see links

Formula

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

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