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%I #10 May 30 2021 15:27:10
%S 2,-1,-7,-7,17,65,65,-127,-511,-511,1025,4097,4097,-8191,-32767,
%T -32767,65537,262145,262145,-524287,-2097151,-2097151,4194305,
%U 16777217,16777217,-33554431,-134217727,-134217727,268435457,1073741825
%N a(n) = A128018(n) + 1.
%C 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.
%H Colin Barker, <a href="/A157240/b157240.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-6,4).
%F G.f.: (2-7*x+8*x^2) / ((1-x)*(4*x^2-2*x+1)).
%F From _Colin Barker_, May 22 2019: (Start)
%F a(n) = (2 + (1-i*sqrt(3))^(1+n) + (1+i*sqrt(3))^(1+n)) / 2 where i=sqrt(-1).
%F a(n) = 3*a(n-1) - 6*a(n-2) + 4*a(n-3) for n>2.
%F (End)
%F a(n) = A138230(n+1)+1. - _R. J. Mathar_, Sep 11 2019
%t LinearRecurrence[{3,-6,4},{2,-1,-7},40] (* _Harvey P. Dale_, May 30 2021 *)
%o (PARI) Vec((2 - 7*x + 8*x^2) / ((1 - x)*(1 - 2*x + 4*x^2)) + O(x^35)) \\ _Colin Barker_, May 22 2019
%Y Cf. A128018, A157241.
%K easy,sign
%O 0,1
%A _Creighton Dement_, Feb 25 2009
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