A141146 Number of linear arrangements of n blue, n red and n green items such that first and last elements are blue but there are no adjacent items of the same color.
0, 2, 14, 96, 664, 4660, 33144, 238448, 1732112, 12685428, 93552700, 694072720, 5176136640, 38777105120, 291661779920, 2201518518240, 16670124621472, 126586920736564, 963723103197516, 7354034055776864, 56236603567496720
Offset: 1
Keywords
Links
- Max Alekseyev, PARI scripts for various problems
- L. Q. Eifler, K. B. Reid Jr., D. P. Roselle, Sequences with adjacent elements unequal, Aequationes Mathematicae 6 (2-3), 1971.
Programs
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PARI
{ a(n) = sum(k=0,n\2, binomial(n-1,2*k) * binomial(2*k,k) * binomial(n-1+k,k+1) * 2^(n-1-2*k) ) }
Formula
a(n) = A110711(n) / 3.
a(n) = Sum[k=0..[n/2]] binomial(n-1,2k) * binomial(2k,k) * binomial(n-1+k,k+1) * 2^(n-1-2k).
G.f.: (2*x-1)^2*(1-8*x)^(-4/3)*(x+1)^(-8/3)*hypergeom([4/3, 4/3],[2],27*x^2/((8*x-1)*(x+1)^2))-(1-8*x)^(-1/3)*(x+1)^(-2/3)*hypergeom([1/3, 1/3],[1],27*x^2/((8*x-1)*(x+1)^2)). - Mark van Hoeij, May 14 2013
Conjecture: -(n+1)*(n-2)*a(n) +(7*n^2-13*n+4)*a(n-1) +8*(n-2)^2*a(n-2)=0. - R. J. Mathar, Jul 23 2014