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A190917
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Number of permutations of n copies of 1..3 introduced in order 1..3 with no element equal to another within a distance of 1.
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11
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1, 1, 5, 29, 182, 1198, 8142, 56620, 400598, 2872754, 20824778, 152303410, 1122149800, 8319825040, 62017475600, 464452683432, 3492568119566, 26358270711370, 199565061455634, 1515311001158482, 11535716330003876, 88025068713285476, 673124069796140900
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OFFSET
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0,3
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LINKS
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FORMULA
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n*(n+1)*a(n) - (n+1)*(7*n-4)*a(n-1) - 8*(n-2)^2*a(n-2) = 0. - R. J. Mathar, Nov 01 2015 from A110706
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EXAMPLE
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All solutions for n=2:
1 1 1 1 1
2 2 2 2 2
3 3 3 3 1
1 2 2 1 3
3 3 1 2 2
2 1 3 3 3
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MAPLE
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a:= proc(n) option remember; `if`(n<3, [1$2, 5][n+1],
((7*n-4)*a(n-1)+8*(n-2)^2*a(n-2)/(n+1))/n)
end:
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MATHEMATICA
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Table[(1/3)*Sum[Binomial[n-1, k]*(Binomial[n-1, k]*Binomial[2*n+1-2*k, n+1] + Binomial[n-1, k+1]*Binomial[2*n-2*k, n+1]), {k, 0, Floor[n/2]}], {n, 1, 25}] (* G. C. Greubel, Nov 24 2018 *)
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PROG
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(PARI) A190917(n) = sum(k=0, n\2, binomial(n-1, k)*(binomial(n-1, k)*binomial(2*n+1-2*k, n+1)+binomial(n-1, k+1)*binomial(2*n-2*k, n+1))) / 3; \\ Max Alekseyev, Dec 10 2017
(Magma) [(&+[Binomial(n-1, k)*(Binomial(n-1, k)*Binomial(2*n+1-2*k, n+1) + Binomial(n-1, k+1)*Binomial(2*n-2*k, n+1)): k in [0..Floor(n/2)]])/3: n in [1..25]]; // G. C. Greubel, Nov 24 2018
(Sage) [(1/3)*sum(binomial(n-1, k)*(binomial(n-1, k)*binomial(2*n+1-2*k, n+1) + binomial(n-1, k+1)*binomial(2*n-2*k, n+1)) for k in range(1+floor(n/2))) for n in (1..25)] # G. C. Greubel, Nov 24 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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