A016826 a(n) = (4n + 2)^2.

4, 36, 100, 196, 324, 484, 676, 900, 1156, 1444, 1764, 2116, 2500, 2916, 3364, 3844, 4356, 4900, 5476, 6084, 6724, 7396, 8100, 8836, 9604, 10404, 11236, 12100, 12996, 13924, 14884, 15876, 16900, 17956

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

A bisection of A016742. Sequence arises from reading the line from 4, in the direction 4, 36, ... in the square spiral whose vertices are the squares A000290. - Omar E. Pol, May 24 2008

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Equals A001539 + 1.

Cf. A000290, A010503, A016742, A016754, A016802, A016814, A016838.

Programs

Maple

A016826:=n->(4*n + 2)^2; seq(A016826(n), n=0..40); # Wesley Ivan Hurt, Feb 24 2014

Mathematica

(4*Range[0,40]+2)^2 (* or *) LinearRecurrence[{3,-3,1},{4,36,100},40] (* Harvey P. Dale, Nov 24 2011 *)

PARI

a(n)=(4*n+2)^2 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = a(n-1) + 32*n (with a(0)=4). - Vincenzo Librandi, Dec 15 2010

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), with a(0)=4, a(1)=36, a(2)=100. - Harvey P. Dale, Nov 24 2011

G.f.: -((4*(x^2+6*x+1))/(x-1)^3). - Harvey P. Dale, Nov 24 2011

a(n) = A000290(A016825(n)). - Wesley Ivan Hurt, Feb 24 2014

From Amiram Eldar, Jun 28 2020: (Start)

Sum_{n>=0} 1/a(n) = Pi^2/32.

Sum_{n>=0} (-1)^n/a(n) = G/4, where G is the Catalan constant (A006752). (End)

From Amiram Eldar, Jan 29 2021: (Start)

Product_{n>=0} (1 + 1/a(n)) = cosh(Pi/4).

Product_{n>=0} (1 - 1/a(n)) = 1/sqrt(2) (A010503). (End)