A235320 - OEIS

%I #15 Aug 12 2017 10:37:41

%S 1,2,6,8,38,102,192,786,2214,4598,17906,51306,112928,425882,1232454,

%T 2818458,10393254,30269862,71152482,257993706,754758738,1811628498,

%U 6482271054,19026456246,46431160992,164353672602,483626452302,1196266880906,4196480707814

%N The number of length n sequences on {0,1,2} such that there are an equal number of 0's and 1's or there are an equal number of 0's and 2's.

%H Alois P. Heinz, <a href="/A235320/b235320.txt">Table of n, a(n) for n = 0..1000</a>

%F For n congruent to 0 mod 3 a(n) = 2*A002426(n) - n!/floor(n/3)!^3.

%F For n congruent to 1 or 2 mod 3 a(n) = 2*A002426(n).

%e a(3) = 8 because we have: 012, 021, 102, 111, 120, 201, 210, 222.

%p a:= proc(n) option remember; `if`(n<6, [1, 2, 6, 8, 38, 102][n+1],

%p      ((n-1)^2*(380713*n^2-2450435*n+3831534) *a(n-1)

%p       -3*(n-2)^2*(230459*n^2-1671772*n+2280969) *a(n-2)

%p       -(811908*n^4-11125602*n^3+47672874*n^2-84737610*n+54621270) *a(n-3)

%p       -27*(n-2)*(n-3)*(380713*n^2-2450435*n+3831534) *a(n-4)

%p       +81*(n-3)*(n-4)*(230459*n^2-1671772*n+2280969) *a(n-5)

%p       +243*(n-3)*(n-4)*(n-5)*(120233*n-220828) *a(n-6)) /

%p       (n^2*(n-1)*(10007*n+17779)))

%p     end:

%p seq(a(n), n=0..40);  # _Alois P. Heinz_, Jan 05 2014

%t Table[2Sum[Multinomial[k,k,n-2k],{k,0,Floor[n/2]}],{n,0,30}]-Riffle[Riffle[Table[Multinomial[n,n,n],{n,0,10}],0],0,3]

%Y Cf. A002426 comment by _Dennis P. Walsh_.

%K nonn,easy

%O 0,2

%A _Geoffrey Critzer_, Jan 05 2014