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A235320
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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.
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1
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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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).
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EXAMPLE
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a(3) = 8 because we have: 012, 021, 102, 111, 120, 201, 210, 222.
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MAPLE
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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:
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MATHEMATICA
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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]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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