1,3

Each term is a sum of two consecutive squares, or a(n) = k^2 + (k+1)^2 for some k. Squares of each term are the hex numbers, or centered hexagonal numbers: a(n) = A001570(n-1) for n>1. - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 14 2008

Gareth Jones and David Singerman, Belyi Functions, Hypermaps and Galois Groups, Bull. London Math. Soc., 28 (1996), 561-590.

Henry MacKean and Victor Moll, Ellipic Curves, Cambridge University Press, New York, 1997, page 22.

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Let M be the 8 X 8 matrix {{0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}, {-1, 0, 0, 0, 14, 0, 0, 0}}; let v[1] = Table[1, {n, 1, 8}], v[n] = M.v[n - 1]; then a(n) =v[4*n][[1]].

a(n)=(1/4)*sqrt(3)*[7-4*sqrt(3)]^n-(1/4)*sqrt(3)*[7+4*sqrt(3)]^n+(1/2)*[7+4*sqrt(3)]^n+(1/2) *[7-4*sqrt(3)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jun 19 2008

G.f.: x*(1-13x)/(1-14*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]

M = {{0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}, {-1, 0, 0, 0, 14, 0, 0, 0}}; v[1] = Table[1, {n, 1, 8}] v[n_] := v[n] = M.v[n - 1] a = Table[v[4*n][[1]], {n, 1, 25}]

This is simply a variant of A001570.

Sequence in context: A127390 A142646 A083576 this_sequence A001570 A020544 A009015

Adjacent sequences: A122568 A122569 A122570 this_sequence A122572 A122573 A122574

nonn

Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 17 2006

Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 21 2006 and Dec 04 2006