0,7

Let [p,q,r] = the three terms in M^n * [1,0,0]. Then f(x),x=1,2,3: of px^2 + qx + r = the next three terms in the sequence. Example: M^2 * [0,0,1] = [3, 7, 13], where (3, 7, 13) = a(7), a(8), a(9). Then 3x^2 + 7x + 13, x=1,2,3 = the next three terms in the sequence: a(10), a(11), a(12) = 23, 39, 61, where M^3 * [0,0,1] = [23, 39, 61]. Likewise, 23x^2 + 39x + 61, x=1,2,3 = a(13), a(14), a(15) = 123, 231, 385; and so on.

A composite wave sequence of the pattern: A122883(n), A122884(n), A122885(n), A122883(n+1), A122884(n+1), A122885(n+1),... Append M^(n+1) * [0,0,1] to the right of M^(n) * [0,0,1] to form an infinite string.

a(n)=4*a(n-3)+11*a(n-6)-2*a(n-9). G.f.: -x^2*(x-1)*(2*x^5-x^4+3*x^2+2*x+1)/((2*x^3+1)*(1-6*x^3+x^6)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 12 2009]

M^0 * [0,0,1] = 0,0,1; M^1 * [0,0,1) = [1,1,1]; M^2 * [0,0,1] = [3,7,13]. Appending, we form a string, A122886: 0, 0, 1, 1, 1, 1, 3, 7, 13...

Cf. A122883, A122884, A122885.

Sequence in context: A053599 A136851 A155339 this_sequence A154691 A078447 A066624

Adjacent sequences: A122883 A122884 A122885 this_sequence A122887 A122888 A122889

nonn,uned

Gary W. Adamson and Roger L. Bagula (qntmpkt(AT)yahoo.com), Sep 17 2006