A141147 Number of linear arrangements of n blue, n red and n green items such that the first item is blue and there are no adjacent items of the same color (first and last elements considered as adjacent).

2, 8, 44, 268, 1732, 11624, 80096, 562748, 4013396, 28964128, 211054120, 1550226880, 11463513440, 85257846080, 637243586944, 4783617720892, 36046416801268, 272543202174704, 2066898899119448, 15717398604230888

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Max Alekseyev, PARI scripts for various problems

L. Q. Eifler, K. B. Reid Jr., and D. P. Roselle, Sequences with adjacent elements unequal, Aequationes Mathematicae 6 (2-3), 1971.

Formula

a(n) = A110707(n) / 3 = (A000172(n) + A000172(n-1)) * 2 / 3.

a(n) = Sum_{k=0..floor(n/2)} binomial(n,2k) * binomial(2k,k) * binomial(n-1+k,k) * 2^(n-2k).

a(n) = 2^n*Hypergeometric([n,(1-n)/2,-n/2],[1, 1],1). - Peter Luschny, Jan 15 2012

Recurrence: (3*n^3 + 13*n^2 + 16*n + 4)*a(n+2) = (21*n^3 + 73*n^2 + 74*n + 16)*a(n+1) + (24*n^3 + 32*n^2)*a(n). - Ralf Stephan, Feb 11 2014

a(n) = (1/n) * Sum_{k = floor(n/2)..n} k * binomial(n,k)^2 * binomial(2*k,n). - Peter Bala, Mar 19 2023

Maple

A141147 := n -> 2^n*hypergeom([n, (1-n)/2, -n/2], [1, 1], 1);
seq(simplify(A141147(i)), i=1..20); # Peter Luschny, Jan 15 2012

Prog

(PARI) { a(n) = sum(k=0, n\2, binomial(n, 2*k) * binomial(2*k, k) * binomial(n-1+k, k) * 2^(n-2*k) ) }

Crossrefs

Cf. A110706, A110707, A110710, A110711, A141146, A141148.

Sequence in context: A121747 A261266 A014508 * A346626 A201374 A120928

Adjacent sequences: A141144 A141145 A141146 * A141148 A141149 A141150

Keyword

nonn

Author

Max Alekseyev, Jun 10 2008

Status

approved