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%I #13 Mar 17 2024 12:00:15
%S 0,2,1,8,7,13,25,27,43,71,85,124,186,260,346,509,716,1002,1434,1989,
%T 2829,4051,5693,8043,11459,16240,23028,32780,46497,66031,93930,133527,
%U 189826,270137,384082,546262,777617,1106381,1574318,2240820,3189344,4539451,6462231
%N Number of compositions of n where the difference between largest and smallest parts equals 2 and adjacent parts are unequal.
%H Alois P. Heinz, <a href="/A214271/b214271.txt">Table of n, a(n) for n = 3..5000</a>
%F 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
%e a(4) = 2: [3,1], [1,3].
%e a(5) = 1: [1,3,1].
%e 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].
%e 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].
%e 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].
%Y Column k=2 of A214269.
%K nonn
%O 3,2
%A _Alois P. Heinz_, Jul 09 2012
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