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A110211 a(n+3) = 6*a(n) - 5*a(n+2), a(0) = -1, a(1) = 3, a(2) = -15. 3

%I

%S -1,3,-15,69,-327,1545,-7311,34593,-163695,774609,-3665487,17345265,

%T -82078671,388400433,-1837930575,8697180849,-41155501647,194749924785,

%U -921566538831,4360899684273,-20635998872655,97650595130289,-462087577545807,2186621894493105

%N a(n+3) = 6*a(n) - 5*a(n+2), a(0) = -1, a(1) = 3, a(2) = -15.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-5, 0, 6).

%F G.f. (1+2*x)/((x-1)*(6*x^2+6*x+1))

%F a(n)=(9-3*Sqrt[3]+(-3-Sqrt[3])^n*(-4+Sqrt[3])+(-3+Sqrt[3])^n*(-5+2*Sqrt[3]))/(13*(-3+Sqrt[3])) [From Harvey P. Dale, Mar 28 2012]

%p seriestolist(series((1+2*x)/((x-1)*(6*x^2+6*x+1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 1kbasesumseq[A*B] with A = + 'i + 'ii' + 'ij' + 'ik' and B = + .5'i - .5'j + .5'k + .5i' + .5j' - .5k' - .5'ij' - .5'ik' + .5'ji' + .5'ki' Sumtype is set to: sum[(Y[0], Y[1], Y[2]),mod(3)

%t LinearRecurrence[{-5,0,6},{-1,3,-15},30] (* _Harvey P. Dale_, Mar 28 2012 *)

%Y Cf. A110210, A110212, A110213.

%K easy,sign

%O 0,2

%A _Creighton Dement_, Jul 16 2005

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Last modified September 16 06:18 EDT 2021. Contains 347469 sequences. (Running on oeis4.)