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A214273 Number of compositions of n where the difference between largest and smallest parts equals 4 and adjacent parts are unequal.

%I A214273 #11 Jan 03 2019 04:33:55
%S A214273 0,2,1,8,12,23,51,90,165,295,550,952,1682,2974,5151,9007,15530,26848,
%T A214273 46194,79404,136092,232622,397633,677892,1154741,1964078,3337218,
%U A214273 5664428,9605090,16274305,27548925,46602325,78775262,133073729,224662007,379067097,639250682
%N A214273 Number of compositions of n where the difference between largest and smallest parts equals 4 and adjacent parts are unequal.
%H A214273 Alois P. Heinz, <a href="/A214273/b214273.txt">Table of n, a(n) for n = 5..2000</a>
%F A214273 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 A214273 a(6) = 2: [5,1]. [1,5].
%e A214273 a(7) = 1: [1,5,1].
%e A214273 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 A214273 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 A214273 Column k=4 of A214269.
%K A214273 nonn
%O A214273 5,2
%A A214273 _Alois P. Heinz_, Jul 09 2012