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

3,2

Links

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

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

Example

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].

Crossrefs

Column k=2 of A214269.

Sequence in context: A340629 A105672 A338249 * A372474 A262007 A005489

Adjacent sequences: A214268 A214269 A214270 * A214272 A214273 A214274

Keyword

nonn

Author

Alois P. Heinz, Jul 09 2012

Status

approved