Search: id:A104099
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%I A104099
%S A104099 0,5,58,219,548,1105,1950,3143,4744,6813,9410,12595,16428,20969,26278,
%T A104099 32415,39440,47413,56394,66443,77620,89985,103598,118519,134808,152525,
%U A104099 171730,192483,214844,238873,264630,292175,321568,352869,386138,421435
%N A104099 n * (10n^2 - 6n + 1), or n*A087348(n).
%C A104099 First entry of the vector (M^n)v, where M is the 4 X 4 matrix [[1,2,1,
               1],[0,1,3,8],[0,0,1,5],[0,0,0,1]] and v is the column vector [[0,
               1,1,2].
%C A104099 Characteristic polynomial of the matrix M is (x-1)^4.
%F A104099 Recurrence relation: a(n)=4a(n-1)-6a(n-2)+4a(n-3)-a(n-4) for n>=4; a(0)=0, 
               a(1)=5, a(2)=58, a(3)=219.
%F A104099 O.g.f.: x*(5+38*x+17*x^2)/(-1+x)^4 = 132/(-1+x)^3+60/(-1+x)^4+89/(-1+x)^2+17/
               (-1+x) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2007
%p A104099 a[0]:=0:a[1]:=5:a[2]:=58:a[3]:=219: for n from 4 to 40 do a[n]:=4*a[n-1]-6*a[n-2]+4*a[n-3]-a[n-4] 
               od: seq(a[n], n=0..40);
%t A104099 M = {{1, 2, 1, 1}, {0, 1, 3, 8}, {0, 0, 1, 5}, {0, 0, 0, 1}}; w[0] = 
               {0, 1, 1, 2}; w[n_] := w[n] = M.w[n - 1] a=Table[w[n][[1]], {n, 0, 
               50}]
%Y A104099 Sequence in context: A009481 A086060 A068003 this_sequence A129897 A151424 
               A097631
%Y A104099 Adjacent sequences: A104096 A104097 A104098 this_sequence A104100 A104101 
               A104102
%K A104099 nonn
%O A104099 0,2
%A A104099 Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 31 2005
%E A104099 Edited by N. J. A. Sloane (njas(AT)research.att.com), May 20 2006, Jun 
               06 2007

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