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%I #51 Jan 29 2024 08:37:53
%S 1,1,13,181,2521,35113,489061,6811741,94875313,1321442641,18405321661,
%T 256353060613,3570537526921,49731172316281,692665874901013,
%U 9647591076297901,134373609193269601,1871582937629476513,26067787517619401581,363077442309042145621,5057016404808970637113
%N a(1)=a(2)=1, a(n) = 14*a(n-1) - a(n-2).
%C Essentially the same as A001570: 1 followed by A001570.
%C 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
%D Henry MacKean and Victor Moll, Elliptic Curves, Cambridge University Press, New York, 1997, page 22.
%H Gareth Jones and David Singerman, <a href="http://blms.oxfordjournals.org/content/28/6/561.extract">Belyi Functions, Hypermaps and Galois Groups</a>, Bull. London Math. Soc., 28 (1996), 561-590.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-1).
%F G.f.: x*(1-13*x)/(1-14*x+x^2). - _Philippe Deléham_, Nov 17 2008
%F a(n+1) = A001570(n). - _Ctibor O. Zizka_, Feb 26 2010
%F a(n) = (1/4)*sqrt(2+(2-sqrt(3))^(4*n-2) + (2+sqrt(3))^(4*n-2)). - _Gerry Martens_, Jun 03 2015
%t LinearRecurrence[{14, -1}, {1, 1}, 25] (* _Paolo Xausa_, Jan 29 2024 *)
%Y Cf. A001570 (essentially the same).
%K nonn,easy
%O 1,3
%A _Roger L. Bagula_, Sep 17 2006
%E Edited by _N. J. A. Sloane_, Sep 21 2006 and Dec 04 2006
%E a(19)-a(21) from _Paolo Xausa_, Jan 29 2024
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