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A108898 a(n+3) = 3*a(n+2) - 2*a(n), a(0) = -1, a(1) = 1, a(2) = 3. 10
-1, 1, 3, 11, 31, 87, 239, 655, 1791, 4895, 13375, 36543, 99839, 272767, 745215, 2035967, 5562367, 15196671, 41518079, 113429503, 309895167, 846649343, 2313089023, 6319476735, 17265131519, 47169216511, 128868696063, 352075825151, 961889042431, 2627929735167, 7179637555199 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,0,-2).

FORMULA

a(n) = A028860(n+2)-1.

G.f.: (-1+4*x)/((x-1)*(2*x^2+2*x-1)).

From Colin Barker, Apr 29 2019: (Start)

a(n) = (-1 + (-(1-sqrt(3))^n + (1+sqrt(3))^n)/sqrt(3)).

a(n) = 3*a(n-1) - 2*a(n-3) for n>2.

(End)

MAPLE

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)

PROG

(Haskell)

a108898 n = a108898_list !! n

a108898_list = -1 : 1 : 3 :

   zipWith (-) (map (* 3) $ drop 2 a108898_list) (map (* 2) a108898_list)

-- Reinhard Zumkeller, Oct 15 2011

(PARI) Vec(-(1 - 4*x) / ((1 - x)*(1 - 2*x - 2*x^2)) + O(x^40)) \\ Colin Barker, Apr 29 2019

CROSSREFS

Cf. A005665, A077846, A028860.

Cf. A002605, A026150, A028859, A030195, A080040, A083337, A106435, A125145.

Sequence in context: A268800 A054343 A320238 * A291887 A217323 A263781

Adjacent sequences:  A108895 A108896 A108897 * A108899 A108900 A108901

KEYWORD

easy,sign

AUTHOR

Creighton Dement, Jul 16 2005

STATUS

approved

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Last modified May 26 22:58 EDT 2020. Contains 334634 sequences. (Running on oeis4.)