A189356 a(n) gives y-values solving the Diophantine equation 2*x^2 + (x-1)^2 = y^2 for positive x.

3, 41, 571, 7953, 110771, 1542841, 21489003, 299303201, 4168755811, 58063278153, 808717138331, 11263976658481, 156886956080403, 2185153408467161, 30435260762459851, 423908497265970753, 5904283700961130691, 82236063316189858921, 1145400602725696894203

Offset: 1

Author

Sture Sjöstedt, May 02 2011

Keywords

• nonn

Comments

(a(n)-1)/2 gives indices of triangular numbers which are also pentagonal (A046175).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (14,-1).

Crossrefs

Cf. A081065, A046174, A046175.

Programs

Magma

[n le 2 select 38*n-35 else 14*Self(n-1)-Self(n-2): n in [1..19]]; // Bruno Berselli, May 03 2011

Mathematica

LinearRecurrence[{14,-1}, {3, 41}, 19]  (* Bruno Berselli, Nov 11 2011 *)

Formula

a(n) = 14*a(n-1) - a(n-2).

G.f.: x*(3-x)/(1-14*x+x^2). - Bruno Berselli, May 03 2011

Extensions

Extended by T. D. Noe, May 02 2011