A235320 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.

1, 2, 6, 8, 38, 102, 192, 786, 2214, 4598, 17906, 51306, 112928, 425882, 1232454, 2818458, 10393254, 30269862, 71152482, 257993706, 754758738, 1811628498, 6482271054, 19026456246, 46431160992, 164353672602, 483626452302, 1196266880906, 4196480707814

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

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

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

Example

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

Maple

a:= proc(n) option remember; `if`(n<6, [1, 2, 6, 8, 38, 102][n+1],
     ((n-1)^2*(380713*n^2-2450435*n+3831534) *a(n-1)
      -3*(n-2)^2*(230459*n^2-1671772*n+2280969) *a(n-2)
      -(811908*n^4-11125602*n^3+47672874*n^2-84737610*n+54621270) *a(n-3)
      -27*(n-2)*(n-3)*(380713*n^2-2450435*n+3831534) *a(n-4)
      +81*(n-3)*(n-4)*(230459*n^2-1671772*n+2280969) *a(n-5)
      +243*(n-3)*(n-4)*(n-5)*(120233*n-220828) *a(n-6)) /
      (n^2*(n-1)*(10007*n+17779)))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Jan 05 2014

Mathematica

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]

Crossrefs

Cf. A002426 comment by Dennis P. Walsh.

Sequence in context: A076507 A117542 A045653 * A152158 A291782 A327271

Adjacent sequences: A235317 A235318 A235319 * A235321 A235322 A235323

Keyword

nonn,easy

Author

Geoffrey Critzer, Jan 05 2014

Status

approved