Search: id:A122365
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%I A122365
%S A122365 0,1,1,6,15,53,160,517,1621,5150,16267,51513,162944,515673,1631609,
%T A122365 5162966,16336695,51693645,163571104,517580093,1637750957,5182251182,
%U A122365 16397926099,51887105969,164183665152,519517828081,1643883210801
%N A122365 The (1,6)-entry of the matrix M^n, where M is the 6 X 6 matrix {{1, 1, 
               1, 1, 1, 1},{1, 0, 0, 0, 1, 0},{1, 0, 0, 1, 0, 0},{1, 0, 1, 0, 0, 
               0},{1, 1, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0}}.
%F A122365 a(n)=2a(n-1)+5a(n-2)-3a(n-3)-4a(n-4)+a(n-5); a(0)=0, a(1)=1, a(2)=1,a(3)=6,
               a(4)=15 (follows from the minimal polynomial of M).
%p A122365 a[0]:=0: a[1]:=1: a[2]:=1: a[3]:=6: a[4]:=15: for n from 5 to 26 do a[n]:=2*a[n-1]+5*a[n-2]-3*a[n-3]-4*a[n-4]\
               +a[n-5] od: seq(a[n],n=0..26);
%t A122365 M = {{1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 1, 0}, {1, 0, 0, 1, 0, 0}, {1, 
               0, 1, 0, 0, 0}, {1, 1, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0}}; v[1] = {0, 
               0, 0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], 
               {n, 1, 50}]
%Y A122365 Sequence in context: A106272 A056423 A056347 this_sequence A146746 A119132 
               A073065
%Y A122365 Adjacent sequences: A122362 A122363 A122364 this_sequence A122366 A122367 
               A122368
%K A122365 nonn
%O A122365 0,4
%A A122365 Gary Adamson and Roger Bagula (qntmpkt(AT)yahoo.com), Oct 19 2006
%E A122365 Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 29 2006

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