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 A125201 #48 Aug 01 2025 16:32:49
%S A125201 1,2,19,52,101,166,247,344,457,586,731,892,1069,1262,1471,1696,1937,
%T A125201 2194,2467,2756,3061,3382,3719,4072,4441,4826,5227,5644,6077,6526,
%U A125201 6991,7472,7969,8482,9011,9556,10117,10694,11287,11896,12521,13162,13819,14492,15181,15886
%N A125201 a(n) = 8*n^2 - 7*n + 1.
%C A125201 Central terms of the triangle in A125199.
%C A125201 Sequence found by reading the line from 2, in the direction 2, 19, ..., in the square spiral whose vertices are the triangular numbers A000217. - _Omar E. Pol_, Sep 05 2011
%C A125201 Maximum number of regions that can be obtained in the plane by drawing n copies of a "strict long-legged M" letter. - _N. J. A. Sloane_, Aug 01 2025
%H A125201 Arkadiusz Wesolowski, <a href="/A125201/b125201.txt">Table of n, a(n) for n = 1..1000</a>
%H A125201 N. J. A. Sloane, <a href="/A125201/a125201.jpg">Two strict long-legged M's can divide the plane into a(2) = 19 regions.</a>
%H A125201 N. J. A. Sloane, <a href="/A125201/a125201_1.jpg">Three strict long-legged M's can divide the plane into a(3) = 52 regions.</a>
%H A125201 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A125201 a(n) = 1 + A051870(n). - _Omar E. Pol_, Sep 05 2011
%F A125201 From _Arkadiusz Wesolowski_, Dec 25 2011: (Start)
%F A125201 a(1) = 2, a(n) = a(n-1) + 16*n - 15.
%F A125201 a(n) = 2*a(n-1) - a(n-2) + 16 with a(1) = 2 and a(2) = 19.
%F A125201 G.f.: (1 - x + 16*x^2)/(1 - x)^3. (End)
%F A125201 Sum_{n>=1} 1/a(n) = (psi(9/16+sqrt(17)/16) - psi(9/16-sqrt(17)/16))/sqrt(17) = 0.61242052... - _R. J. Mathar_, Apr 22 2024
%F A125201 From _Elmo R. Oliveira_, Oct 31 2024: (Start)
%F A125201 E.g.f.: exp(x)*(8*x^2 + x + 1) - 1.
%F A125201 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%t A125201 Table[8*n^2 - 7*n + 1, {n, 44}] (* _Arkadiusz Wesolowski_, Feb 15 2012 *)
%o A125201 (Magma) [8*n^2-7*n+1:n in [1..44]]; // _Vincenzo Librandi_, Dec 27 2010
%o A125201 (PARI) a(n)=8*n^2-7*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A125201 Cf. A000217, A051870, A125199.
%K A125201 nonn,easy
%O A125201 0,2
%A A125201 _Reinhard Zumkeller_, Nov 24 2006
%E A125201 a(0) = 1 added by _N. J. A. Sloane_, Aug 01 2025 (this will require several additional changes).