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 A242587 The number of conjugacy classes of n X n matrices over F_3. 13
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Apparently the Euler transform of A001867. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 K. E. Morrison, Integer sequences and matrices over finite fields, J. Int. Seq. 9 (2006) # 06.2.1, Section 1.16. FORMULA 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=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 MAPLE A242587 := proc(n) 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): seq(a(n), n=0..50); # Alois P. Heinz, Sep 07 2014 MATHEMATICA 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 *) (O[x]^20 - 2/QPochhammer[3, x])[[3]] (* Vladimir Reshetnikov, Nov 20 2015 *) PROG (Maxima) S(n, m):=if n=0 then 1 else if n

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Last modified December 1 06:17 EST 2022. Contains 358454 sequences. (Running on oeis4.)