A157286 a(n) = 36*n^2 - n.

35, 142, 321, 572, 895, 1290, 1757, 2296, 2907, 3590, 4345, 5172, 6071, 7042, 8085, 9200, 10387, 11646, 12977, 14380, 15855, 17402, 19021, 20712, 22475, 24310, 26217, 28196, 30247, 32370, 34565, 36832, 39171, 41582, 44065, 46620, 49247, 51946

Offset

1,1

Comments

From Vincenzo Librandi, Jan 28 2012: (Start)

The identity (10368*n^2 - 288*n + 1)^2 - (36*n^2 - n)*(1728*n - 24)^2 = 1 can be written as A157288(n)^2 - a(n)*A157287(n)^2 = 1; this is the case s=6 of the identity (8*n^2*s^4 - 8*n*s^2 + 1)^2 - (n^2*s^2 - n)*(8*n*s^3 - 4*s)^2 = 1.

Also, the identity (72*n - 1)^2 - (36*n^2 - n)*12^2 = 1 can be written as A157921(n)^2 - a(n)*12^2 = 1 (see Barbeau's paper). (End)

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 14 in the first table at p. 85, case d(t) = t*(6^2*t-1)).

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).

G.f.: x*(37*x + 35)/(1-x)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {35, 142, 321}, 40] (* Vincenzo Librandi, Jan 28 2012 *)
Table[36n^2-n, {n, 40}] (* Harvey P. Dale, Jan 27 2020 *)

Prog

(Magma) [36*n^2-n: n in [1..40]]
(PARI) a(n)=(6*n)^2-n \\ Charles R Greathouse IV, Dec 27 2011

Crossrefs

Cf. A157287, A157288, A157921.

Sequence in context: A330230 A330233 A220014 * A354543 A324072 A327901

Adjacent sequences: A157283 A157284 A157285 * A157287 A157288 A157289

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 26 2009

Status

approved