OFFSET
0,2
COMMENTS
Floretion Algebra Multiplication Program, FAMP Code: 1tesseq[ + 'ij' + 'ik' + 'ji' + 'jk' + 'ki' + 'kj' + e]
a(n) = term (1,1) in M^n, M = the 4 X 4 matrix [1, 1, 1, 2; 1, 1, 2, 1; 1, 2, 1, 1; 2, 1, 1, 1]. a(n)/a(n-1) tends to 5, a root to the charpoly x^4 - 4x^3 - 6x^2 + 4x + 5. - Gary W. Adamson, Mar 12 2009
This is 1+A003463(n+1) rounded down to the next odd integer. - R. J. Mathar, Sep 11 2019
LINKS
Robert Munafo, Sequences Related to Floretions
Index entries for linear recurrences with constant coefficients, signature (5,1,-5).
FORMULA
a(n) = 4*a(n-1) + 5*a(n-2) - 2 (conjecture). - Creighton Dement, Apr 13 2005
(1/4) (5^(n+1) - 2(-1)^2 + 1). - Ralf Stephan, May 17 2007
From R. J. Mathar, Mar 19 2009: (Start)
G.f.: -(-1 - 2*x + 5*x^2)/((x-1)*(5*x-1)*(1+x)).
a(n) = 5*a(n-1) + a(n-2) - 5*a(n-3). (End)
MATHEMATICA
a = Table[Sum[5^i, {i, 0, n}] + 1 - Mod[Sum[5^i, {i, 0, n}], 2], {n, 0, 50}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Mar 15 2005
STATUS
approved