A144555 a(n) = 14*n^2.

0, 14, 56, 126, 224, 350, 504, 686, 896, 1134, 1400, 1694, 2016, 2366, 2744, 3150, 3584, 4046, 4536, 5054, 5600, 6174, 6776, 7406, 8064, 8750, 9464, 10206, 10976, 11774, 12600, 13454, 14336, 15246, 16184, 17150, 18144, 19166, 20216, 21294, 22400, 23534, 24696

Offset: 0

Author

N. J. A. Sloane, Jan 01 2009

Keywords

• nonn
• easy

Comments

Sequence found by reading the line from 0, in the direction 0, 14, ..., in the square spiral whose vertices are the generalized enneagonal numbers A118277. Also sequence found by reading the same line and direction in the square spiral whose edges have length A195019 and whose vertices are the numbers A195020. - Omar E. Pol, Sep 10 2011

Links

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

Crossrefs

See also A033428, A033429, A033581, A033582, A033583, A033584, ... and A249327 for the whole table.

Cf. A000290, A001105, A064761, A118277, A152742, A195019, A195020.

Cf. A008596, A195145.

Programs

Mathematica

Table[14*n^2, {n, 0, 45}] (* Amiram Eldar, Feb 03 2021 *)

PARI

A144555(n)=14*n^2 \\ M. F. Hasler, Oct 31 2014

Formula

a(n) = 14*A000290(n) = 7*A001105(n) = 2*A033582(n). - Omar E. Pol, Jan 01 2009

a(n) = a(n-1) + 14*(2*n-1), with a(0) = 0. - Vincenzo Librandi, Nov 25 2010

From Amiram Eldar, Feb 03 2021: (Start)

Sum_{n>=1} 1/a(n) = Pi^2/84.

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/168.

Product_{n>=1} (1 + 1/a(n)) = sqrt(14)*sinh(Pi/sqrt(14))/Pi.

Product_{n>=1} (1 - 1/a(n)) = sqrt(14)*sin(Pi/sqrt(14))/Pi. (End)

From Elmo R. Oliveira, Nov 30 2024: (Start)

G.f.: 14*x*(1 + x)/(1-x)^3.

E.g.f.: 14*x*(1 + x)*exp(x).

a(n) = n*A008596(n) = A195145(2*n).

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