A323111 Number of compositions of 2n where the difference between largest and smallest parts equals n.

0, 2, 3, 12, 23, 61, 135, 306, 679, 1499, 3257, 7053, 15167, 32443, 69080, 146533, 309743, 652762, 1371897, 2876284, 6017100, 12562511, 26180328, 54469099, 113151406, 234723068, 486276265, 1006195365, 2079647131, 4293758081, 8856361762, 18250277543

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..200

Formula

a(n) = A214258(2n,n).

Conjecture: a(n) ~ n * 2^(n-3). - Vaclav Kotesovec, Jan 07 2019

Example

a(2) = 2: 13, 31.
a(3) = 3: 114, 141, 411.
a(4) = 12: 1115, 1151, 1511, 5111, 125, 152, 215, 251, 512, 521, 26, 62.
a(5) = 23: 11116, 11161, 11611, 16111, 61111, 1126, 1162, 1216, 1261, 1612, 1621, 2116, 2161, 2611, 6112, 6121, 6211, 136, 163, 316, 361, 613, 631.

Crossrefs

Cf. A117989 (the same for partitions), A214258.

Sequence in context: A323125 A323126 A323127 * A302545 A320173 A107928

Adjacent sequences: A323108 A323109 A323110 * A323112 A323113 A323114

Keyword

nonn

Author

Alois P. Heinz, Jan 04 2019

Status

approved