A158370 576n + 1.

577, 1153, 1729, 2305, 2881, 3457, 4033, 4609, 5185, 5761, 6337, 6913, 7489, 8065, 8641, 9217, 9793, 10369, 10945, 11521, 12097, 12673, 13249, 13825, 14401, 14977, 15553, 16129, 16705, 17281, 17857, 18433, 19009, 19585, 20161, 20737, 21313

Offset

1,1

Comments

The identity (576*n+1)^2-(576*n^2+2*n)*(24)^2=1 can be written as a(n)^2-A158369(n)*(24)^2=1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

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*(24^2*t+2)).

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

G.f.: x*(577-x)/(1-x)^2.

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

Mathematica

LinearRecurrence[{2, -1}, {577, 1153}, 50]

Prog

(Magma) I:=[577, 1153]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 576*n + 1.

Crossrefs

Cf. A158369.

Sequence in context: A234499 A218039 A218157 * A244095 A261889 A031726

Adjacent sequences: A158367 A158368 A158369 * A158371 A158372 A158373

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 17 2009

Status

approved