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%I #34 Jan 25 2021 02:47:54
%S 0,16,64,144,256,400,576,784,1024,1296,1600,1936,2304,2704,3136,3600,
%T 4096,4624,5184,5776,6400,7056,7744,8464,9216,10000,10816,11664,12544,
%U 13456,14400,15376,16384,17424,18496,19600,20736,21904,23104,24336,25600,26896
%N a(n) = (4*n)^2.
%C A bisection of A016742. Sequence arises from reading the line from 0, in the direction 0, 16, ... in the square spiral whose vertices are the squares A000290. - _Omar E. Pol_, May 24 2008
%C Also, sequence found by reading the line from 0, in the direction 0, 16, ... in the square spiral whose vertices are the generalized decagonal numbers A074377. - _Omar E. Pol_, Sep 10 2011
%H Ivan Panchenko, <a href="/A016802/b016802.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 16*n^2 = A000290(n)*16. - _Omar E. Pol_, Dec 11 2008
%F a(n) = A001105(n)*8 = A016742(n)*4 = A139098(n)*2. - _Omar E. Pol_, Dec 13 2008
%F a(n) = a(n-1) + 16*(2*n-1) (with a(0)=0). - _Vincenzo Librandi_, Nov 20 2010
%F From _Amiram Eldar_, Jan 25 2021: (Start)
%F Sum_{n>=1} 1/a(n) = Pi^2/96.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/192.
%F Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/4)/(Pi/4).
%F Product_{n>=1} (1 - 1/a(n)) = sin(Pi/4)/(Pi/4) = 2*sqrt(2)/Pi (A112628). (End)
%o (PARI) a(n) = (4*n)^2; \\ _Michel Marcus_, Mar 04 2014
%Y Cf. A000290, A001539, A016742, A016754, A016814, A016826, A016838, A001105, A112628, A139098.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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