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A242587
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The number of conjugacy classes of n X n matrices over F_3.
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19
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1, 3, 12, 39, 129, 399, 1245, 3783, 11514, 34734, 104754, 314922, 946623, 2842077, 8532147, 25603788, 76830033, 230513439, 691598901, 2074870002, 6224790639, 18674600664, 56024355396, 168073769199, 504222998115, 1512671142432, 4538018555652, 13614062210490
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OFFSET
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0,2
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COMMENTS
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Apparently the Euler transform of A001867.
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LINKS
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FORMULA
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G.f.: 1/Product_{r>=1} (1-3*x^r).
a(n) = S(n,1), where S(n,m) = sum(k=m..n/2, 3*S(n-k,k))+3, S(n,n)=3, S(0,m)=1, S(n,m)=0 for n<m. - Vladimir Kruchinin, Sep 07 2014
a(n) ~ c * 3^n, where c = Product_{k>=1} 1/(1-1/3^k) = 1.7853123419985341903674... . - Vaclav Kotesovec, Mar 19 2015
G.f.: Sum_{i>=0} 3^i*x^i/Product_{j=1..i} (1 - x^j). - Ilya Gutkovskiy, Apr 12 2018
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MAPLE
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local r, x ;
if n = 0 then
1;
else
1/mul(1-3*x^r, r=1..n) ;
convert(%, parfrac, x) ;
coeftayl(%, x=0, n) ;
end if;
end proc:
# second Maple program:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1) +`if`(i>n, 0, 3*b(n-i, i))))
end:
a:= n-> b(n$2):
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, 3*b[n-i, i]]]] ; a[n_] := b[n, n]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Apr 03 2015, after Alois P. Heinz *)
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PROG
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(Maxima)
S(n, m):=if n=0 then 1 else if n<m then 0 else if n=m then 3 else sum(3*S(n-k, k), k, m, n/2)+3;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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