A185950 a(n) = 4*n^2 - n - 1.

-1, 2, 13, 32, 59, 94, 137, 188, 247, 314, 389, 472, 563, 662, 769, 884, 1007, 1138, 1277, 1424, 1579, 1742, 1913, 2092, 2279, 2474, 2677, 2888, 3107, 3334, 3569, 3812, 4063, 4322, 4589, 4864, 5147, 5438, 5737, 6044, 6359, 6682, 7013, 7352, 7699, 8054, 8417, 8788, 9167, 9554, 9949, 10352, 10763, 11182, 11609

Offset: 0

Author

Paul Curtz, Feb 07 2011

Keywords

• sign
• easy

Comments

Write the sequence A023443 in a clockwise spiral. a(n) is on the y-axis.

a(n) mod 9 = period 9: repeat [8,2,4,5,5,4,2,8,4] = A182868(n+2) mod 9.

Examples

			  11--12--13--14--15
   |               |
  10   1---2---3  16
   |   |       |   |
   9   0-(-1)  4  17
   |           |   |
   8---7---6---5  18
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A033951, A182868.

Programs

Haskell

a185950 n = (4 * n - 1) * n - 1 -- Reinhard Zumkeller, Aug 14 2013

Magma

[-1-n+4*n^2: n in [0..80]]; // Vincenzo Librandi, Feb 08 2011

Maple

A185950:=n->4*n^2-n-1: seq(A185950(n), n=0..100); # Wesley Ivan Hurt, Jan 30 2017

Mathematica

Table[4n^2-n-1,{n,0,60}] (* or *) LinearRecurrence[{3,-3,1},{-1,2,13},60] (* Harvey P. Dale, May 22 2015 *)

PARI

a(n)=4*n^2-n-1 \\ Charles R Greathouse IV, Dec 21 2011

Formula

a(n) = A176126(4*n-1) = A054556(n+1) - 2 = A033991(n) - 1.

a(n) = a(n-1) + 8*n - 5.

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

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

G.f.: ( 1-5*x-4*x^2 ) / (x-1)^3. - R. J. Mathar, Feb 10 2011

E.g.f.: (4*x^2 + 3*x - 1)*exp(x). - G. C. Greubel, Jul 23 2017