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

0,2

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

Table of n, a(n) for n=0..42.

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

Formula

a(n) = A000290(n)*14 = A001105(n)*7 = A033582(n)*2. - 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)

Mathematica

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

Prog

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

Crossrefs

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

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

Sequence in context: A140784 A022285 A100157 * A192846 A212347 A115129

Adjacent sequences: A144552 A144553 A144554 * A144556 A144557 A144558

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 01 2009

Status

approved