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 A144555 a(n) = 14*n^2. 22
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified May 7 20:36 EDT 2021. Contains 343652 sequences. (Running on oeis4.)