OFFSET
0,1
COMMENTS
Floretion Algebra Multiplication Program, FAMP Code: 2tesforseq[A*B], with A = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' and B = + .5'ij' + .5'ji'; 1vesforseq(n) = (-1)^(n+1)*2, ForType: 1A
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-4,-4,-1).
FORMULA
a(n) + a(n+1) = (-1)^(n+1)*A001906(n) = (-1)^(n+1)*F(2n).
From Colin Barker, May 01 2019: (Start)
a(n) = -(2^(-1-n)*(5*(-1)^n*2^(3+n) + (-3-sqrt(5))^n*(-5+sqrt(5)) - (-3+sqrt(5))^n*(5+sqrt(5)))) / 5.
a(n) = -4*a(n-1) - 4*a(n-2) - a(n-3) for n>2. (End)
MATHEMATICA
CoefficientList[Series[-(3+9x+2x^2)/((x+1)(x^2+3x+1)), {x, 0, 40}], x] (* or *) LinearRecurrence[{-4, -4, -1}, {-3, 3, -2}, 40] (* Harvey P. Dale, Jun 22 2022 *)
PROG
(PARI) Vec(-(3 + 9*x + 2*x^2) / ((1 + x)*(1 + 3*x + x^2)) + O(x^35)) \\ Colin Barker, May 01 2019
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Creighton Dement, Aug 30 2007
EXTENSIONS
Definition corrected (by negating prior formula) by Harvey P. Dale, Jun 22 2022
STATUS
approved