OFFSET
0,1
COMMENTS
Generating floretion is Y = .5('i + 'j + 'k + i' + j' + k') + ee. ("tes"). Note: A current conjecture is that if X is a floretion for which 4*tes(X^n) is an integer for all n, then X+sigma(X) also has this property. "sigma" is the uniquely defined projection operator which "flips the arrows" of a floretion (i.e. sigma('i) = i', sigma('j) = j', etc.). Taking X = .5('i + 'j + 'k + ee), then tesseq(X) = [ -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, ...] is an integer sequence, thus by the conjecture 4*tes(Y^n) = 4*tes((X+sigma)^n) should also be an integer sequence for all n.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-6,4).
FORMULA
G.f.: (2-7*x+8*x^2) / ((1-x)*(4*x^2-2*x+1)).
From Colin Barker, May 22 2019: (Start)
a(n) = (2 + (1-i*sqrt(3))^(1+n) + (1+i*sqrt(3))^(1+n)) / 2 where i=sqrt(-1).
a(n) = 3*a(n-1) - 6*a(n-2) + 4*a(n-3) for n>2.
(End)
a(n) = A138230(n+1)+1. - R. J. Mathar, Sep 11 2019
MATHEMATICA
LinearRecurrence[{3, -6, 4}, {2, -1, -7}, 40] (* Harvey P. Dale, May 30 2021 *)
PROG
(PARI) Vec((2 - 7*x + 8*x^2) / ((1 - x)*(1 - 2*x + 4*x^2)) + O(x^35)) \\ Colin Barker, May 22 2019
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Creighton Dement, Feb 25 2009
STATUS
approved