A158070 a(n) = 64*n^2 + 2*n.

0, 66, 260, 582, 1032, 1610, 2316, 3150, 4112, 5202, 6420, 7766, 9240, 10842, 12572, 14430, 16416, 18530, 20772, 23142, 25640, 28266, 31020, 33902, 36912, 40050, 43316, 46710, 50232, 53882, 57660, 61566, 65600, 69762, 74052, 78470, 83016

Offset

0,2

Comments

The identity (64*n + 1)^2 - (64*n^2 + 2*n)*8^2 = 1 can be written as A158071(n)^2 - a(n)*8^2 = 1. - Vincenzo Librandi, Feb 11 2012

Links

Ray Chandler, Table of n, a(n) for n = 0..10000 (corrected by Ray Chandler, Jan 19 2019)

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*(8^2*t+2)).

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), a(1)=66, a(2)=260, a(3)=582. - Harvey P. Dale, Jul 25 2011 [corrected by M. F. Hasler, Oct 09 2014]

G.f.: x*(66 + 62*x)/(1-x)^3. - Vincenzo Librandi, Feb 11 2012

Mathematica

Table[64n^2+2n, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {66, 260, 582}, 40] (* Harvey P. Dale, Jul 25 2011 *)

Prog

(Magma) I:=[66, 260, 582]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 11 2012
(PARI) for(n=1, 50, print1(64*n^2 + 2*n", ")); \\ Vincenzo Librandi, Feb 11 2012

Crossrefs

Cf. A158071.

Sequence in context: A268582 A117306 A322768 * A242726 A271739 A251055

Adjacent sequences: A158067 A158068 A158069 * A158071 A158072 A158073

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 12 2009

Extensions

Extended to a(0)=0 by M. F. Hasler, Oct 09 2014

Status

approved