This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A016802 #49 Nov 30 2024 14:26:16
%S A016802 0,16,64,144,256,400,576,784,1024,1296,1600,1936,2304,2704,3136,3600,
%T A016802 4096,4624,5184,5776,6400,7056,7744,8464,9216,10000,10816,11664,12544,
%U A016802 13456,14400,15376,16384,17424,18496,19600,20736,21904,23104,24336,25600,26896,28224
%N A016802 a(n) = (4*n)^2.
%C A016802 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 A016802 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 A016802 Karl-Heinz Hofmann, <a href="/A016802/b016802.txt">Table of n, a(n) for n = 0..10000</a> (first 200 terms from Ivan Panchenko).
%H A016802 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A016802 a(n) = 16*n^2 = 16*A000290(n). - _Omar E. Pol_, Dec 11 2008
%F A016802 a(n) = 8*A001105(n) = 4*A016742(n) = 2*A139098(n). - _Omar E. Pol_, Dec 13 2008
%F A016802 a(n) = a(n-1) + 16*(2*n-1) (with a(0)=0). - _Vincenzo Librandi_, Nov 20 2010
%F A016802 From _Amiram Eldar_, Jan 25 2021: (Start)
%F A016802 Sum_{n>=1} 1/a(n) = Pi^2/96.
%F A016802 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/192.
%F A016802 Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/4)/(Pi/4).
%F A016802 Product_{n>=1} (1 - 1/a(n)) = sin(Pi/4)/(Pi/4) = 2*sqrt(2)/Pi (A112628). (End)
%F A016802 From _Elmo R. Oliveira_, Nov 30 2024: (Start)
%F A016802 G.f.: 16*x*(1 + x)/(1-x)^3.
%F A016802 E.g.f.: 16*x*(1 + x)*exp(x).
%F A016802 a(n) = n*A008598(n) = A195146(2*n).
%F A016802 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%o A016802 (PARI) a(n) = (4*n)^2; \\ _Michel Marcus_, Mar 04 2014
%o A016802 (Python)
%o A016802 def A016802(n): return (4*n)**2 # _Karl-Heinz Hofmann_, Sep 11 2024
%Y A016802 Cf. A000290, A001105, A001539, A016742, A016754, A016814, A016826, A016838, A112628.
%Y A016802 Cf. A008598, A074377, A139098, A195146.
%K A016802 nonn,easy
%O A016802 0,2
%A A016802 _N. J. A. Sloane_