1,2

Characteristic polynomial is x^4 - 4x^3 -42x^2 - 36x + 81. a(n)/a(n-1) tends to 9. Squareroot of M = the 4 X 4 matrix: [1/u, 1, u, 1; 1, 1/u, 1, u; u, 1, 1/u, 1; 1, u, 1, 1/u]; where u, 1/u and 1 are the cyclotomic third roots of Unity: (-1, + sqrt(3)i)/2, (-1, -sqrt(3)i)/2 and 1.

Squares of A046717 terms, deleting the first "1" of A046717. a(n) = leftmost term in M^n * [1,0,0,0] where M is the 4 X 4 matrix: [1,-2,4,-2; -2,1,-2,4; 4,-2,1,-2; -2,4,-2,1].

G.f.: x(1+18x-27x^2)/((1-x)(1-9x)(1+3x)). a(n) = 7a(n-1) +21a(n-2) -27a(n-3). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 09 2008]

a(4) = 1681 = 41^2 = the square of A046717(4)

a(4) = 1681 since M^4 * [1,0,0,0] = [1681, -1640, 1600, -1640].

Cf. A046717.

Sequence in context: A080109 A017126 A007204 this_sequence A115330 A145964 A020250

Adjacent sequences: A120093 A120094 A120095 this_sequence A120097 A120098 A120099

nonn

Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 08 2006