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A144555
a(n) = 14*n^2.
23
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
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
See also A033428, A033429, A033581, A033582, A033583, A033584, ... and A249327 for the whole table.
Sequence in context: A140784 A022285 A100157 * A192846 A212347 A115129
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 01 2009
STATUS
approved