%I A094943
%S A094943 1,13,72,429,2601,15534,93339,559845,3359232,20155473,120932109,
%T A094943 725594598,4353563943,26121388761,156728328192,940369966965,
%U A094943 5642219821473,33853318876350,203119913356515,1218719480001309
%N A094943 A sequence generated from a semi-magic square.
%C A094943 The 3 rows: 1 3 2, 2 1 3 and 3 2 1 form a semi-magic square; with rows, 
               columns and a diagonal having a sum of 6. a(n)/a(n-1) tends to 6, 
               an eigenvalue of the matrix. E.g.: a(7)/a(6) = 93339/15534 = 6.0086... 
               A094944 uses the same format and operations but has different terms.
%F A094943 G.f.: (1+10*x+18*x^2)/(1-3*x-18*x^3-15*x^2); a(n+3)=3*a(n+2)+15*a(n+1)+18*a(n), 
               a(0) = 1, a(1) = 13, a(2) = 72. - Alec Mihailovs, Aug 28 2005
%F A094943 Let [1 3 2 / 2 1 3 / 3 2 1] = the 3 X 3 matrix M. Take M^n * [1 0 0] 
               = [p q r]; then a(n) = p.
%e A094943 a(4) = 429 since M^4 * [1 0 0] = [429 q r]
%t A094943 a[n_] := (MatrixPower[{{1, 3, 2}, {2, 1, 3}, {3, 2, 1}}, n].{{1}, {0}, 
               {0}})[[1, 1]]; Table[ a[n], {n, 10}] (from Robert G. Wilson v May 
               29 2004)
%Y A094943 Cf. A094944, A109467.
%Y A094943 Sequence in context: A096913 A026916 A106173 this_sequence A000470 A107141 
               A139849
%Y A094943 Adjacent sequences: A094940 A094941 A094942 this_sequence A094944 A094945 
               A094946
%K A094943 nonn
%O A094943 1,2
%A A094943 Gary W. Adamson (qntmpkt(AT)yahoo.com), May 25 2004
%E A094943 Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), May 29 
               2004