Search: id:A102105
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%I A102105
%S A102105 1,12,83,486,2645,13872,71303,362346,1829225,9198612,46150523,231225006,
%T A102105 1157542205,5791962552,28972567343,144901100466,724620293585,
%U A102105 3623445841692,18118262329763,90594411012726,452981353155365
%N A102105 (1/4) [19*5^n - 16*3^n + 1 ].
%C A102105 Sum of the entries in the last row of the 3 X 3 matrix M^n, where M={{1 
               0 0}{2 3 0 }{ 3 4 5}}.
%C A102105 Sum of the entries in the second row of M^n = A048473(n).
%F A102105 a(n) = 9a(n-1) - 23a(n-2) + 15a(n-3), a(0)=1,a(1)=12,a(2)=83 (derived 
               from the minimal polynomial of the matrix M).
%e A102105 a(4) = 2645 = 9*486 - 23*83 + 15*12 = 9*a(3) - 23*a(2) + 15*a(1).
%e A102105 a(4) = 2645 since M^4 * [1 1 1] = [1 161 2645], where 161 = A048473(4).
%p A102105 with(linalg): M[1]:=matrix(3,3,[1,0,0,2,3,0,3,4,5]): for n from 2 to 
               23 do M[n]:=multiply(M[1],M[n-1]) od: 1,seq(multiply(M[n],matrix(3,
               1,[1,1,1]))[3,1],n=1..23);
%Y A102105 Cf. A000326, A094727, A048473.
%Y A102105 Sequence in context: A163020 A164300 A175037 this_sequence A026949 A165127 
               A075476
%Y A102105 Adjacent sequences: A102102 A102103 A102104 this_sequence A102106 A102107 
               A102108
%K A102105 nonn
%O A102105 0,2
%A A102105 Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 30 2004
%E A102105 Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
%E A102105 Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 02 2006
%E A102105 New definition from Ralf Stephan, May 17 2007

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