0,2

a(n)/a(n-1) tends to the largest eigenvalue of the matrix: (1 + Cos Pi/9) = 2.87938524157... A005578 can be generated by A^n * [1,0,0,0,0,0], leftmost nonzero term.

Fan Chung and Shlomo Sternberg, "Mathematics and the Buckyball". Fan Chung Graham homepage.

Let A = the 6x2 adjacency matrix of a benzene ring (ref.): [0,1,0,0,0,1; 1,0,1,0,0,0; 0,1,0,1,0,0; 0,0,1,0,1,0; 0,0,0,1,0,1; 1,0,0,0,1,0]. Then perform M = A^2 - A = [2,-1,1,0,1,-1; -1,2,-1,1,0,1; 1,-1,2,-1,1,0; 0,1,-1,2,-1,1; 1,0,1,-1,2,-1; -1,1,0,1,-1,2]. a(n) = leftmost term in M^n * [1,0,0,0,0,0].

a(5) = 30 = leftmost term in M^5 * [1,0,0,0,0,0].

Cf. A005578.

Sequence in context: A119268 A002989 A000671 this_sequence A013326 A074663 A113122

Adjacent sequences: A120259 A120260 A120261 this_sequence A120263 A120264 A120265

nonn

Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 14 2006