A185918 a(n) = 12*n^2 - 2*n - 1.

-1, 9, 43, 101, 183, 289, 419, 573, 751, 953, 1179, 1429, 1703, 2001, 2323, 2669, 3039, 3433, 3851, 4293, 4759, 5249, 5763, 6301, 6863, 7449, 8059, 8693, 9351, 10033, 10739, 11469, 12223, 13001, 13803, 14629, 15479, 16353, 17251, 18173, 19119, 20089, 21083, 22101, 23143, 24209

Offset: 0

Author

Paul Curtz, Feb 08 2011

Keywords

• sign
• easy

Comments

The second quadrisection of A184005(n-1) is A179741(n).

The first quadrisection of A184005(n-1) is a(n).

Sequence found by reading the line from -1, in the direction -1, 9, ..., in the square spiral whose vertices are -1 together with the generalized octagonal numbers A001082. - Omar E. Pol, Jul 18 2012

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. A001082, A154106, A179741, A184005.

Programs

Magma

[-1-2*n+12*n^2: n in [0..80] ]; // Vincenzo Librandi, Feb 09 2011

Maple

A185918:=n->12*n^2-2*n-1: seq(A185918(n), n=0..60); # Wesley Ivan Hurt, Jan 31 2017

Mathematica

Table[12n^2-2n-1,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{-1,9,43},50] (* Harvey P. Dale, May 20 2012 *)

PARI

a(n)=12*n^2-2*n-1 \\ Charles R Greathouse IV, Dec 21 2011

Formula

a(n) = A184005(4*n-1). [corrected by R. J. Mathar, Aug 24 2011]

a(n) = a(n-1) + 24*n - 14.

a(n) = 2*a(n-1) - a(n) + 24.

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

G.f.: -(1+x)*(13*x-1) / (x-1)^3. - R. J. Mathar, Aug 24 2011

a(n) = A154106(n-1) - 2, n >= 1. - Omar E. Pol, Jul 19 2012

E.g.f.: (12*x^2 + 10*x -1)*exp(x). - G. C. Greubel, Jul 22 2017

Extensions

More terms from Vincenzo Librandi, Feb 09 2011