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

1,2

Links

Table of n, a(n) for n=1..21.

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.

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

Prog

(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) ) }

Crossrefs

Cf. A110706, A110707, A110710, A110711, A141147, A141148.

Sequence in context: A066052 A122057 A164891 * A267913 A204699 A286445

Adjacent sequences: A141143 A141144 A141145 * A141147 A141148 A141149

Keyword

nonn

Author

Max Alekseyev, Jun 10 2008

Status

approved