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A158136
a(n) = 144*n - 1.
2
143, 287, 431, 575, 719, 863, 1007, 1151, 1295, 1439, 1583, 1727, 1871, 2015, 2159, 2303, 2447, 2591, 2735, 2879, 3023, 3167, 3311, 3455, 3599, 3743, 3887, 4031, 4175, 4319, 4463, 4607, 4751, 4895, 5039, 5183, 5327, 5471, 5615, 5759, 5903, 6047, 6191
OFFSET
1,1
COMMENTS
The identity (144*n - 1)^2 - (144*n^2 - 2*n)*12^2 = 1 can be written as a(n)^2 - A158135(n)*12^2 = 1. - Vincenzo Librandi, Feb 11 2012
LINKS
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*(12^2*t-2)).
FORMULA
G.f.: x*(143+x)/(1-x)^2. - Vincenzo Librandi, Feb 11 2012
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 11 2012
MATHEMATICA
144Range[50]-1 (* Harvey P. Dale, Feb 14 2011 *)
LinearRecurrence[{2, -1}, {143, 287}, 50] (* Vincenzo Librandi, Feb 11 2012 *)
PROG
(Magma) I:=[143, 287]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 11 2012
(PARI) for(n=1, 40, print1(144*n - 1", ")); \\ Vincenzo Librandi, Feb 11 2012
CROSSREFS
Cf. A158135.
Sequence in context: A353059 A176876 A257767 * A153874 A003902 A261074
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 13 2009
STATUS
approved