A125201 a(n) = 8*n^2 - 7*n + 1.

2, 19, 52, 101, 166, 247, 344, 457, 586, 731, 892, 1069, 1262, 1471, 1696, 1937, 2194, 2467, 2756, 3061, 3382, 3719, 4072, 4441, 4826, 5227, 5644, 6077, 6526, 6991, 7472, 7969, 8482, 9011, 9556, 10117, 10694, 11287, 11896, 12521, 13162, 13819, 14492, 15181, 15886

Offset

1,1

Comments

Central terms of the triangle in A125199.

Sequence found by reading the line from 2, in the direction 2, 19, ..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 05 2011

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 1 + A051870(n). - Omar E. Pol, Sep 05 2011

From Arkadiusz Wesolowski, Dec 25 2011: (Start)

a(1) = 2, a(n) = a(n-1) + 16*n - 15.

a(n) = 2*a(n-1) - a(n-2) + 16 with a(1) = 2 and a(2) = 19.

G.f.: (1 - x + 16*x^2)/(1 - x)^3. (End)

Sum_{n>=1} 1/a(n) = (psi(9/16+sqrt(17)/16) - psi(9/16-sqrt(17)/16))/sqrt(17) = 0.61242052... - R. J. Mathar, Apr 22 2024

From Elmo R. Oliveira, Oct 31 2024: (Start)

E.g.f.: exp(x)*(8*x^2 + x + 1) - 1.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)

Mathematica

Table[8*n^2 - 7*n + 1, {n, 44}] (* Arkadiusz Wesolowski, Feb 15 2012 *)

Prog

(Magma) [8*n^2-7*n+1:n in [1..44]]; // Vincenzo Librandi, Dec 27 2010
(PARI) a(n)=8*n^2-7*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A000217, A051870, A125199.

Sequence in context: A031911 A136685 A226489 * A215392 A340558 A140544

Adjacent sequences: A125198 A125199 A125200 * A125202 A125203 A125204

Keyword

nonn,easy

Author

Reinhard Zumkeller, Nov 24 2006

Status

approved