The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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: A369442 A320238 A369399 * A291887 A217323 A263781 Adjacent sequences: A108895 A108896 A108897 * A108899 A108900 A108901 KEYWORD easy,sign AUTHOR Creighton Dement, Jul 16 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 24 23:50 EDT 2024. Contains 372782 sequences. (Running on oeis4.)