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%I #14 Apr 29 2019 09:42:21
%S -1,1,3,11,31,87,239,655,1791,4895,13375,36543,99839,272767,745215,
%T 2035967,5562367,15196671,41518079,113429503,309895167,846649343,
%U 2313089023,6319476735,17265131519,47169216511,128868696063,352075825151,961889042431,2627929735167,7179637555199
%N a(n+3) = 3*a(n+2) - 2*a(n), a(0) = -1, a(1) = 1, a(2) = 3.
%C In reference to the program code, "ibasek" corresponds to the floretion 'ik'. Sequences in this same batch are "kbase" = A005665 (Tower of Hanoi with cyclic moves only.) and "ibase" = A077846.
%H Reinhard Zumkeller, <a href="/A108898/b108898.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-2).
%F a(n) = A028860(n+2)-1.
%F G.f.: (-1+4*x)/((x-1)*(2*x^2+2*x-1)).
%F From _Colin Barker_, Apr 29 2019: (Start)
%F a(n) = (-1 + (-(1-sqrt(3))^n + (1+sqrt(3))^n)/sqrt(3)).
%F a(n) = 3*a(n-1) - 2*a(n-3) for n>2.
%F (End)
%p seriestolist(series((-1+4*x)/((x-1)*(2*x^2+2*x-1)), x=0,31)); -or- Floretion Algebra Multiplication Program, FAMP Code: 2ibaseksumseq[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)
%o (Haskell)
%o a108898 n = a108898_list !! n
%o a108898_list = -1 : 1 : 3 :
%o zipWith (-) (map (* 3) $ drop 2 a108898_list) (map (* 2) a108898_list)
%o -- _Reinhard Zumkeller_, Oct 15 2011
%o (PARI) Vec(-(1 - 4*x) / ((1 - x)*(1 - 2*x - 2*x^2)) + O(x^40)) \\ _Colin Barker_, Apr 29 2019
%Y Cf. A005665, A077846, A028860.
%Y Cf. A002605, A026150, A028859, A030195, A080040, A083337, A106435, A125145.
%K easy,sign
%O 0,3
%A _Creighton Dement_, Jul 16 2005
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