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Number of compositions of n where the difference between largest and smallest parts equals three.
2

%I #6 Jan 07 2019 13:38:35

%S 0,0,2,3,12,23,58,123,266,557,1168,2400,4911,9982,20196,40643,81499,

%T 162899,324678,645404,1280042,2533565,5005449,9872464,19442206,

%U 38234945,75096856,147324049,288705896,565201569,1105475313,2160338661,4218403428,8230986025

%N Number of compositions of n where the difference between largest and smallest parts equals three.

%H Alois P. Heinz, <a href="/A323120/b323120.txt">Table of n, a(n) for n = 3..3509</a>

%F a(n) ~ c * d^n, where d = A086088 = 1.92756197548292530426190586173662216869855... is the real root of the equation d^4 - d^3 - d^2 - d - 1 = 0 and c = 0.566342887702651534849280952809003081138499070062015666102331676335... is the real root of the equation 563*c^4 - 563*c^3 + 174*c^2 - 22*c + 1 = 0. - _Vaclav Kotesovec_, Jan 07 2019

%Y Column k=3 of A214258.

%K nonn

%O 3,3

%A _Alois P. Heinz_, Jan 05 2019