The On-Line Encyclopedia of Integer Sequences (OEIS)

A016826 revision #39

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

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OFFSET

0,1

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).

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)

MAPLE