OFFSET
0,2
COMMENTS
A floretion-generated sequence relating NSW and Pell numbers.
Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[B*C} with B = - .25'i + .25'j + .5'k - .25i' + .25j' + .5k' - .5'kk' - .25'ik' - .25'jk' - .25'ki' - .25'kj' - .5e and C = + .5'i - .25'j + .25'k + .5i' - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Robert Munafo, Sequences Related to Floretions
Index entries for linear recurrences with constant coefficients, signature (2,2,-2,-1).
FORMULA
a(n) = (u^(n+1)+1)*(v^(n+1)+1)/2 with u = 1+sqrt(2), v = 1-sqrt(2). - Vladeta Jovovic, May 30 2007
From Colin Barker, Apr 29 2019: (Start)
G.f.: (1 + 2*x - 3*x^2 - 2*x^3) / ((1 - x)*(1 + x)*(1 - 2*x - x^2)).
a(n) = (1 + (-1)^(1+n) + (1-sqrt(2))^(1+n) + (1+sqrt(2))^(1+n)) / 2.
a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) for n>3.
(End)
PROG
(PARI) Vec((1 + 2*x - 3*x^2 - 2*x^3) / ((1 - x)*(1 + x)*(1 - 2*x - x^2)) + O(x^30)) \\ Colin Barker, Apr 29 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Creighton Dement, Jan 06 2005; revised Aug 22 2005
STATUS
approved