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A379277
Number of solid partitions with multiplicities of parts matching the n-th composition in standard order.
10
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, Python program.
FORMULA
a(2^k) = A000219(k+1).
a(2^k-1) = A207542(k) for k > 0.
From John Tyler Rascoe, Jan 30 2026: (Start)
a(2^k + j) = a(2^k + j + 2^(k-1)) for k > 0 and 0 <= j < 2^(k-1) - 1.
a(2^k+1) = A090984(k). (End)
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
KEYWORD
nonn
AUTHOR
John Tyler Rascoe, Dec 19 2024
STATUS
approved