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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, 26067787517619401581, 363077442309042145621, 5057016404808970637113 (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
FORMULA
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
LinearRecurrence[{14, -1}, {1, 1}, 25] (* Paolo Xausa, Jan 29 2024 *)
CROSSREFS
Cf. A001570 (essentially the same).
Sequence in context: A083576 A189432 A001570 * A239902 A020544 A009015
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Sep 17 2006
EXTENSIONS
Edited by N. J. A. Sloane, Sep 21 2006 and Dec 04 2006
a(19)-a(21) from Paolo Xausa, Jan 29 2024
STATUS
approved

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Last modified March 28 11:46 EDT 2024. Contains 371241 sequences. (Running on oeis4.)