A103645 G.f.: (108*x^2+27*x+1)/(1+2*x-6*x^2-27*x^3).

1, 25, 64, 49, 961, 100, 6889, 12769, 18496, 225625, 4489, 1844164, 2430481, 6325225, 51724864, 124609, 480881041, 435556900, 2017536889, 11562055729, 741146176, 122363538025, 71895305689, 610401563524, 2514384233761

Offset: 0

Author

Creighton Dement, Feb 12 2005

Keywords

• easy
• nonn

Comments

A floretion-generated sequence of squares. This sequence is related to several other sequences of squares.

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.

Links

• Index entries for linear recurrences with constant coefficients, signature (-2,6,27).

Crossrefs

Cf. A103644.

Programs

Mathematica

CoefficientList[ Series[(108x^2 + 27x + 1)/(1 + 2x - 6x^2 - 27x^3), {x, 0, 25}], x] (* Robert G. Wilson v, Feb 12 2005 *)
LinearRecurrence[{-2,6,27},{1,25,64},30] (* Harvey P. Dale, Jul 04 2022 *)

Formula

a(n) = -2*a(n-1) + 6*a(n-2) + 27*a(n-3) with a(0) = 1, a(1) = 25, a(2) = 64.