A395261 Self-convolution of A000293.

1, 2, 9, 28, 88, 250, 706, 1886, 4958, 12620, 31545, 77120, 185502, 438588, 1022377, 2350008, 5335202, 11969160, 26562098, 58340530, 126913276, 273577034, 584692360, 1239460350, 2607259832, 5444266882, 11288922942, 23251902844, 47586826524, 96795128832

Offset

0,2

Comments

Conjecturally, log(a(n)) ~ 2^(1/4) * C_3 * n^(3/4) as n -> infinity, where C_3 = 1.822... is the asymptotic constant for solid partitions (i.e., log(A000293(n)) ~ C_3 * n^(3/4)).

Links

Thomas DiFiore, Table of n, a(n) for n = 0..50

Nicolas Destainville and Suresh Govindarajan, Estimating the asymptotics of solid partitions, arXiv:1406.5605 [cond-mat.stat-mech], 2014; J. Stat. Phys. 158 (2015) 950-967.

Formula

a(n) = Sum_{k=0..n} A000293(k) * A000293(n-k).

Example

a(3) = A000293(0)*A000293(3) + A000293(1)*A000293(2) + A000293(2)*A000293(1) + A000293(3)*A000293(0) = 1*10 + 1*4 + 4*1 + 10*1 = 28.

Crossrefs

Cf. A000293.

Sequence in context: A192693 A368217 A360479 * A258347 A382613 A323957

Adjacent sequences: A395258 A395259 A395260 * A395262 A395263 A395264

Keyword

nonn

Author

Thomas DiFiore, Apr 17 2026

Status

approved