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%I #22 Mar 07 2024 16:02:14
%S 1,25,64,49,961,100,6889,12769,18496,225625,4489,1844164,2430481,
%T 6325225,51724864,124609,480881041,435556900,2017536889,11562055729,
%U 741146176,122363538025,71895305689,610401563524,2514384233761
%N G.f.: (108*x^2+27*x+1)/(1+2*x-6*x^2-27*x^3).
%C A floretion-generated sequence of squares. This sequence is related to several other sequences of squares.
%C Floretion Algebra Multiplication Program, FAMP Code: 4ibaseiseq[ x*(+ 'i + 'j + i' + j' + 'ii' + 'jj' + 'ij' + 'ji' + e) ] where x is the sum of all (16) floretion basis vectors.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,6,27).
%F a(n) = -2*a(n-1) + 6*a(n-2) + 27*a(n-3) with a(0) = 1, a(1) = 25, a(2) = 64.
%t CoefficientList[ Series[(108x^2 + 27x + 1)/(1 + 2x - 6x^2 - 27x^3), {x, 0, 25}], x] (* _Robert G. Wilson v_, Feb 12 2005 *)
%t LinearRecurrence[{-2,6,27},{1,25,64},30] (* _Harvey P. Dale_, Jul 04 2022 *)
%Y Cf. A103644.
%K easy,nonn
%O 0,2
%A _Creighton Dement_, Feb 12 2005
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