cp's OEIS Frontend

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).

%I A141147 #28 Mar 23 2023 03:33:07
%S A141147 2,8,44,268,1732,11624,80096,562748,4013396,28964128,211054120,
%T A141147 1550226880,11463513440,85257846080,637243586944,4783617720892,
%U A141147 36046416801268,272543202174704,2066898899119448,15717398604230888
%N 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).
%H A141147 Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI scripts for various problems</a>
%H A141147 L. Q. Eifler, K. B. Reid Jr., and D. P. Roselle, <a href="http://dx.doi.org/10.1007/BF01819761">Sequences with adjacent elements unequal</a>, Aequationes Mathematicae 6 (2-3), 1971.
%F A141147 a(n) = A110707(n) / 3 = (A000172(n) + A000172(n-1)) * 2 / 3.
%F A141147 a(n) = Sum_{k=0..floor(n/2)} binomial(n,2k) * binomial(2k,k) * binomial(n-1+k,k) * 2^(n-2k).
%F A141147 a(n) = 2^n*Hypergeometric([n,(1-n)/2,-n/2],[1, 1],1). - _Peter Luschny_, Jan 15 2012
%F A141147 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
%F A141147 a(n) = (1/n) * Sum_{k = floor(n/2)..n} k * binomial(n,k)^2 * binomial(2*k,n). - _Peter Bala_, Mar 19 2023
%p A141147 A141147 := n -> 2^n*hypergeom([n, (1-n)/2, -n/2],[1, 1],1);
%p A141147 seq(simplify(A141147(i)),i=1..20); # _Peter Luschny_, Jan 15 2012
%o A141147 (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) ) }
%Y A141147 Cf. A110706, A110707, A110710, A110711, A141146, A141148.
%K A141147 nonn
%O A141147 1,1
%A A141147 _Max Alekseyev_, Jun 10 2008