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A214272 Number of compositions of n where the difference between largest and smallest parts equals 3 and adjacent parts are unequal.

%I A214272 #15 Jan 03 2019 04:15:51
%S A214272 0,2,1,8,12,18,46,69,111,208,340,539,910,1497,2403,3924,6331,10230,
%T A214272 16531,26591,42652,68595,110195,176458,282895,452990,725036,1160067,
%U A214272 1855376,2966265,4740385,7574822,12099506,19324253,30856321,49260709,78631609,125495919
%N A214272 Number of compositions of n where the difference between largest and smallest parts equals 3 and adjacent parts are unequal.
%H A214272 Alois P. Heinz, <a href="/A214272/b214272.txt">Table of n, a(n) for n = 4..2000</a>
%F A214272 a(n) ~ c * d^n, where d = 1.59406371344091594038982448... is the root of the equation -3 + d - 3*d^2 - 3*d^4 + d^5 - 2*d^6 + d^7 - d^8 + d^9 = 0, and c = 0.63168955798354197444724247228159886565558573072349896252... . - _Vaclav Kotesovec_, Sep 01 2014
%e A214272 T(5) = 2: [4,1], [1,4].
%e A214272 T(6) = 1: [1,4,1].
%e A214272 T(7) = 8: [5,2], [4,2,1], [4,1,2], [2,5], [2,4,1], [2,1,4], [1,4,2], [1,2,4].
%e A214272 T(8) = 12: [4,3,1], [4,1,3], [4,1,2,1], [3,4,1], [3,1,4], [2,1,4,1], [1,4,3], [1,4,2,1], [1,4,1,2], [1,3,4], [1,2,4,1], [1,2,1,4].
%Y A214272 Column k=3 of A214269.
%K A214272 nonn
%O A214272 4,2
%A A214272 _Alois P. Heinz_, Jul 09 2012