A103646 G.f.: 9*(3x+1)/(1+2x-6x^2-27x^3).

9, 9, 36, 225, 9, 2304, 1521, 11025, 49284, 8649, 576081, 230400, 3229209, 10478169, 4639716, 140778225, 29192409, 911556864, 2153052801, 1951430625, 33627490884, 2586027609, 249281516961, 424895385600, 715721076009, 7848531119529

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

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-2,6,27).

Crossrefs

Cf. A103644, A103645.

Programs

Mathematica

CoefficientList[ Series[9(3x + 1)/(1 + 2x - 6x^2 - 27x^3), {x, 0, 25}], x] (* Robert G. Wilson v, Feb 12 2005 *)
LinearRecurrence[{-2,6,27},{9,9,36},40] (* Harvey P. Dale, Mar 14 2016 *)

Formula

a(n+3) = -2a(n+2) + 6a(n+1) + 27a(n), a(0) = 9, a(1) = 9, a(2) = 36

a(n) = 9*A103644(n).

4*3^(n+1) = 2*A103644(n) + a(n) + A103645(n) = 11*A103644(n) + A103645(n).

a(n) = A110523(n+2)^2. - R. J. Mathar, Sep 11 2019

Extensions

Corrected and extended by Robert G. Wilson v, Feb 12 2005