A139570 a(n) = 2*n*(n+3).

0, 8, 20, 36, 56, 80, 108, 140, 176, 216, 260, 308, 360, 416, 476, 540, 608, 680, 756, 836, 920, 1008, 1100, 1196, 1296, 1400, 1508, 1620, 1736, 1856, 1980, 2108, 2240, 2376, 2516, 2660, 2808, 2960, 3116, 3276, 3440, 3608, 3780, 3956, 4136, 4320, 4508, 4700, 4896

Offset

0,2

Comments

Numbers n such that 2*n+9 is a square. - Vincenzo Librandi, Nov 24 2010

a(n) appears also as the fourth member of the quartet [p0(n), p1(n), p2(n), a(n)] of the square of [n, n+1, n+2, n+3] in the Clifford algebra Cl_2 for n >= 0. p0(n) = -A147973(n+3), p1 = A046092(n) and p2(n) = A054000(n+1). See a comment on A147973, also with a reference. - Wolfdieter Lang, Oct 15 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = A028552(n)*2 = 2*n^2+6n = n(2n+6).

a(n) = a(n-1)+4*n+4 (with a(0)=0). - Vincenzo Librandi, Nov 24 2010

a(n) = A022998(n) * A022998(n+3). - Paul Curtz, Mar 27 2011

a(n) = 4 * A000096(n). - Paul Curtz, Mar 27 2011

G.f.: 4*x*(2 - x)/(1 - x)^3. - Arkadiusz Wesolowski, Dec 31 2011

From Amiram Eldar, Dec 23 2022: (Start)

Sum_{n>=1} 1/a(n) = 11/36.

Sum_{n>=1} (-1)^(n+1)/a(n) = log(2)/3 - 5/36. (End)

Mathematica

CoefficientList[Series[4 x (2 - x)/(1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, May 23 2014 *)

Prog

(PARI) a(n)=2*n*(n+3) \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A001105, A028552, A046092, A054000, A067728.

Sequence in context: A348093 A186293 A158865 * A265207 A004118 A082231

Adjacent sequences: A139567 A139568 A139569 * A139571 A139572 A139573

Keyword

easy,nonn

Author

Omar E. Pol, May 19 2008

Status

approved