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A107840 a(n)= 3*a(n-1) -3*a(n-3) +a(n-4), n>6. 0

%I

%S 1,1,1,0,4,8,25,63,169,440,1156,3024,7921,20735,54289,142128,372100,

%T 974168,2550409,6677055,17480761,45765224,119814916,313679520,

%U 821223649,2149991423,5628750625,14736260448,38580030724,101003831720

%N a(n)= 3*a(n-1) -3*a(n-3) +a(n-4), n>6.

%F lim a(n)/a(n-1) = 1+(Sqrt[5]+1)/2.

%F G.f.: x*(2*x^2-6*x^4+2*x^5+2*x-1)/( (x-1)* (1+x)*(x^2-3*x+1)). [Sep 28 2009]

%F a(n) = -1/2-9*(-1)^n/10 +7*A001906(n+1)/5 -18*A001906(n)/5, n>2 [Sep 28 2009]

%t (* method one*) F[1] = 1; F[2] = 1; F[3] = 1; F[4] = 0; F[n__] := F[n] = -3*F[n - 1] + 3*F[n - 3] + F[n - 4] a = Table[Abs[F[n]], {n, 1, 50}] an = Table[N[a[[n]]/a[[n - 1]]], {n, 6, 25}] (* method two*) M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 3, 0, -3}} v[1] = {1, 1, 1, 0} v[n_] := v[n] = M.v[n - 1] a0 = Table[Abs[v[n][[1]]], {n, 1, 50}] an = Table[N[a0[[n]]/a0[[n - 1]]], {n, 6, 25}] Det[M - x*IdentityMatrix[4]]

%K nonn,easy

%O 1,5

%A _Roger L. Bagula_, Jun 12 2005

%E Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009

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Last modified August 10 14:50 EDT 2020. Contains 336381 sequences. (Running on oeis4.)