A214273 - OEIS

%I #11 Jan 03 2019 04:33:55

%S 0,2,1,8,12,23,51,90,165,295,550,952,1682,2974,5151,9007,15530,26848,

%T 46194,79404,136092,232622,397633,677892,1154741,1964078,3337218,

%U 5664428,9605090,16274305,27548925,46602325,78775262,133073729,224662007,379067097,639250682

%N Number of compositions of n where the difference between largest and smallest parts equals 4 and adjacent parts are unequal.

%H Alois P. Heinz, <a href="/A214273/b214273.txt">Table of n, a(n) for n = 5..2000</a>

%F a(n) ~ c * d^n, where d = 1.67058061397048614428193473494469299002584... is the root of the equation -4 + 5*d - 9*d^2 + 8*d^3 - 12*d^4 + 9*d^5 - 11*d^6 + 8*d^7 - 9*d^8 + 6*d^9 - 5*d^10 + 3*d^11 - 2*d^12 + d^13 = 0, c = 0.5575332183681935160094360162291847580554... . - _Vaclav Kotesovec_, Sep 01 2014

%e a(6) = 2: [5,1]. [1,5].

%e a(7) = 1: [1,5,1].

%e a(8) = 8: [6,2], [5,2,1], [5,1,2], [2,6], [2,5,1], [2,1,5], [1,5,2], [1,2,5].

%e a(9) = 12: [5,3,1], [5,1,3], [5,1,2,1], [3,5,1], [3,1,5], [2,1,5,1], [1,5,3], [1,5,2,1], [1,5,1,2], [1,3,5], [1,2,5,1], [1,2,1,5].

%Y Column k=4 of A214269.

%K nonn

%O 5,2

%A _Alois P. Heinz_, Jul 09 2012