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 A122571 a(1)=a(2)=1, a(n) = 14*a(n-1) - a(n-2). 2
 1, 1, 13, 181, 2521, 35113, 489061, 6811741, 94875313, 1321442641, 18405321661, 256353060613, 3570537526921, 49731172316281, 692665874901013, 9647591076297901, 134373609193269601, 1871582937629476513 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Essentially the same as A001570: 1 followed by A001570. 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, Apr 14 2008 REFERENCES Henry MacKean and Victor Moll, Elliptic Curves, Cambridge University Press, New York, 1997, page 22. LINKS Gareth Jones and David Singerman, Belyi Functions, Hypermaps and Galois Groups, Bull. London Math. Soc., 28 (1996), 561-590. Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (14,-1). FORMULA 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, Jun 19 2008 G.f.: x*(1-13*x)/(1-14*x+x^2). [Philippe Deléham, Nov 17 2008] a(n+1) = A001570(n). [Ctibor O. Zizka, Feb 26 2010] a(n) = 1/4*sqrt(2+(2-sqrt(3))^(4*n-2)+(2+sqrt(3))^(4*n-2)). - Gerry Martens, Jun 03 2015 MATHEMATICA 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}] CROSSREFS Cf. A001570 (essentially the same). Sequence in context: A201607 A083576 A189432 * A001570 A239902 A020544 Adjacent sequences:  A122568 A122569 A122570 * A122572 A122573 A122574 KEYWORD nonn,easy AUTHOR Roger L. Bagula, Sep 17 2006 EXTENSIONS Edited by N. J. A. Sloane, Sep 21 2006 and Dec 04 2006 STATUS approved

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Last modified December 10 19:01 EST 2018. Contains 318049 sequences. (Running on oeis4.)