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

Author

Alois P. Heinz, Jan 04 2019

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Formula

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

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