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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. 2
0, 2, 14, 96, 664, 4660, 33144, 238448, 1732112, 12685428, 93552700, 694072720, 5176136640, 38777105120, 291661779920, 2201518518240, 16670124621472, 126586920736564, 963723103197516, 7354034055776864, 56236603567496720 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
Sequence in context: A066052 A122057 A164891 * A267913 A204699 A286445
KEYWORD
nonn
AUTHOR
Max Alekseyev, Jun 10 2008
STATUS
approved

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Last modified February 27 04:33 EST 2024. Contains 370362 sequences. (Running on oeis4.)