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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

Table of n, a(n) for n=1..18.

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 June 28 17:15 EDT 2017. Contains 288839 sequences.