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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
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 (list; graph; refs; listen; history; text; internal format)
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 A095239

Adjacent sequences:  A235317 A235318 A235319 * A235321 A235322 A235323

KEYWORD

nonn,easy

AUTHOR

Geoffrey Critzer, Jan 05 2014

STATUS

approved

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Last modified April 18 12:42 EDT 2019. Contains 322209 sequences. (Running on oeis4.)