A258721 a(n) = 24*n^2 + 52*n + 29.

29, 105, 229, 401, 621, 889, 1205, 1569, 1981, 2441, 2949, 3505, 4109, 4761, 5461, 6209, 7005, 7849, 8741, 9681, 10669, 11705, 12789, 13921, 15101, 16329, 17605, 18929, 20301, 21721, 23189, 24705, 26269, 27881, 29541, 31249, 33005, 34809, 36661, 38561, 40509

Offset: 0

Author

Reinhard Zumkeller, Jun 08 2015

Keywords

• nonn
• easy

Comments

First differences of A079588.

6*a(n) - 5 is a square. Therefore, this is the quadrisection of the sequence which lists the numbers m such that 6*m-5 is a square (without 1): 1, 5, 9, 21, 29, 49, 61, 89, 105, 141, 161, 205, 229, ... . [Bruno Berselli, Jun 08 2015]

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A079588.

Programs

Haskell

a258721 n = 4 * n * (6 * n + 13) + 29

Magma

[24*n^2+52*n+29: n in (0..50)] // Bruno Berselli, Jun 08 2015

Mathematica

Table[24 n^2 + 52 n + 29, {n, 0, 50}] (* Bruno Berselli, Jun 08 2015 *)

Maxima

makelist(24*n^2+52*n+29, n, 0, 50); /* Bruno Berselli, Jun 08 2015 */

PARI

vector(50, n, n--; 24*n^2+52*n+29) \\ Bruno Berselli, Jun 08 2015

Sage

[24*n^2+52*n+29 for n in (0..50)] # Bruno Berselli, Jun 08 2015

Formula

G.f.: (29 + 18*x + x^2)/(1 - x)^3.