A158399 784n - 1.

783, 1567, 2351, 3135, 3919, 4703, 5487, 6271, 7055, 7839, 8623, 9407, 10191, 10975, 11759, 12543, 13327, 14111, 14895, 15679, 16463, 17247, 18031, 18815, 19599, 20383, 21167, 21951, 22735, 23519, 24303, 25087, 25871, 26655, 27439, 28223

Offset

1,1

Comments

The identity (784*n-1)^2-(784*n^2-2*n)*28^2=1 can be written as a(n)^2-A158398(n)*28^2=1.

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*(28^2*t-2)).

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

Formula

G.f.: x*(783+x)/(1-x)^2.

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

Mathematica

LinearRecurrence[{2, -1}, {783, 1567}, 50]
784*Range[40]-1 (* Harvey P. Dale, Aug 18 2022 *)

Prog

(Magma) I:=[783, 1567]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 784*n - 1.

Crossrefs

Cf. A158398.

Sequence in context: A238925 A045074 A204279 * A007243 A146978 A095954

Adjacent sequences: A158396 A158397 A158398 * A158400 A158401 A158402

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved