OFFSET
1,1
COMMENTS
The identity (36*n - 1)^2 - (36*n^2 - 2*n)*6^2 = 1 can be written as (A044102(n+1) - 1)^2 - a(n)*6^2 = 1. - Vincenzo Librandi, Feb 11 2012
The continued fraction expansion of sqrt(a(n)) is [6n-1; {1, 4, 1, 12n-2}]. - Magus K. Chu, Nov 08 2022
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(6^2*t-2)).
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: x*(-34 - 38*x)/(x-1)^3. - Vincenzo Librandi, Feb 11 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 11 2012
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {34, 140, 318}, 50] (* Vincenzo Librandi, Feb 11 2012 *)
PROG
(Magma)[36*n^2 - 2*n: n in [1..50]]
(PARI) for(n=1, 50, print1(36*n^2 - 2*n ", ")); \\ Vincenzo Librandi, Feb 11 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 12 2009
STATUS
approved