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A062205
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Number of alignments of n strings of length 4.
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4
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1, 1, 321, 699121, 5552351121, 117029959485121, 5402040231378569121, 480086443888959812703121, 74896283763383392805211587121, 19133358944433370977791260580721121, 7581761490297442738124283591348762605121, 4461925444770180839552702516305804230194739121
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OFFSET
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0,3
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COMMENTS
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Conjectures: a(n) == 1 (mod 80); for fixed k, the sequence a(n) (mod k) eventually becomes periodic. - Peter Bala, Dec 19 2019
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LINKS
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FORMULA
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a(n) ~ 2^(5*n-3) * n!^4 / (Pi^(3/2) * n^(3/2) * 3^n * (log(2))^(4*n+1)).
a(n) ~ sqrt(Pi) * 2^(5*n-1) * n^(4*n+1/2) / (3^n * exp(4*n) * (log(2))^(4*n+1)).
(End)
It appears that a(n) = (1/(2*6^n))*Sum_{k = 0..n} (-1)^(n-k)*binomial(n,k) *A055203(n+k) for n >= 1. - Peter Bala, Dec 19 2019
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MATHEMATICA
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With[{r = 4}, Flatten[{1, Table[Sum[Sum[(-1)^i*Binomial[j, i]*Binomial[j - i, r]^k, {i, 0, j}], {j, 0, k*r}], {k, 1, 15}]}]] (* Vaclav Kotesovec, Mar 22 2016 *)
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CROSSREFS
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See A062204 for references, formulas and comments.
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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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