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A123189 a(1)=1; a(2)=1; a(3)=6; a(n)=3a(n-1)+3a(n-2)-4a(n-3) for n >=4. 0

%I

%S 1,1,6,17,65,222,793,2785,9846,34721,122561,432462,1526185,5385697,

%T 19005798,67069745,236683841,835237566,2947485241,10401433057,

%U 36705804630,129531772097,457106997953,1613093091630,5692473180361

%N a(1)=1; a(2)=1; a(3)=6; a(n)=3a(n-1)+3a(n-2)-4a(n-3) for n >=4.

%p a[1]:=1: a[2]:=1: a[3]:=6: for n from 4 to 25 do a[n]:=3*a[n-1]+3*a[n-2]-4*a[n-3] od: seq(a[n],n=1..25);

%t M = {{1, -2, 1}, {-2, 2, 0}, {1, 1, 0}} v[1] = {1, 0, 0} v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]

%K nonn

%O 1,3

%A _Roger L. Bagula_, Oct 03 2006

%E Edited by _N. J. A. Sloane_, Oct 08 2006

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Last modified July 28 17:15 EDT 2021. Contains 346335 sequences. (Running on oeis4.)