A214271 Number of compositions of n where the difference between largest and smallest parts equals 2 and adjacent parts are unequal.

0, 2, 1, 8, 7, 13, 25, 27, 43, 71, 85, 124, 186, 260, 346, 509, 716, 1002, 1434, 1989, 2829, 4051, 5693, 8043, 11459, 16240, 23028, 32780, 46497, 66031, 93930, 133527, 189826, 270137, 384082, 546262, 777617, 1106381, 1574318, 2240820, 3189344, 4539451, 6462231

Offset: 3

Author

Alois P. Heinz, Jul 09 2012

Keywords

• nonn

Examples

			a(4) = 2: [3,1], [1,3].
a(5) = 1: [1,3,1].
a(6) = 8: [4,2], [3,2,1], [3,1,2], [2,4], [2,3,1], [2,1,3], [1,3,2], [1,2,3].
a(7) = 7: [3,1,3], [3,1,2,1], [2,1,3,1], [1,3,2,1], [1,3,1,2], [1,2,3,1], [1,2,1,3].
a(8) = 13: [5,3], [3,5], [3,2,1,2], [3,1,3,1], [2,4,2], [2,3,2,1], [2,3,1,2], [2,1,3,2], [2,1,2,3], [1,3,1,3], [1,3,1,2,1], [1,2,3,2], [1,2,1,3,1].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..5000

Crossrefs

Column k=2 of A214269.

Formula

a(n) ~ c * d^n, where d = 1.42405422074094158891999182454432643651250048913477... is the root of the equation d^5 - d^4 + d^3 - 2*d^2 + d - 2 = 0 and c = 0.7949863587395197228140209096861039705690343740923239... is the root of the equation -16 + 581*c - 7278*c^2 + 36113*c^3 - 74523*c^4 + 49682*c^5 = 0. - Vaclav Kotesovec, May 01 2014, updated Mar 17 2024