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 A188135 #41 Sep 02 2025 11:01:28 %S A188135 1,11,37,79,137,211,301,407,529,667,821,991,1177,1379,1597,1831,2081, %T A188135 2347,2629,2927,3241,3571,3917,4279,4657,5051,5461,5887,6329,6787, %U A188135 7261,7751,8257,8779,9317,9871,10441,11027,11629,12247,12881,13531,14197,14879,15577,16291,17021,17767 %N A188135 a(n) = 8*n^2 + 2*n + 1. %C A188135 Bisection of A193867. - _Omar E. Pol_, Aug 16 2011 %C A188135 Sequence found by reading the line from 1, in the direction 1, 11, ..., in the square spiral whose vertices are the triangular numbers A000217. - _Omar E. Pol_, Sep 04 2011 %H A188135 Kelvin Voskuijl, <a href="/A188135/b188135.txt">Table of n, a(n) for n = 0..10000</a> %H A188135 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A188135 First differences: a(n) - a(n-1) = 16*n - 6 = A113770(n) = 2*A004770(n). %F A188135 Second differences: a(n) - 2*a(n-1) + a(n-2) = 16. %F A188135 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). %F A188135 From _R. J. Mathar_, Apr 06 2011: (Start) %F A188135 G.f.: -(1+x)*(7*x+1)/(x-1)^3. %F A188135 a(n) = A084849(2*n). (End) %F A188135 E.g.f.: exp(x)*(1 + 10*x + 8*x^2). - _Elmo R. Oliveira_, Oct 19 2024 %o A188135 (Magma) [1 + 2*n + 8*n^2: n in [0..50]]; // _Vincenzo Librandi_, Mar 30 2011 %o A188135 (PARI) a(n)=8*n^2+2*n+1 \\ _Charles R Greathouse IV_, Oct 07 2015 %Y A188135 Cf. A000217, A004770, A084849, A113770, A185438, A193867. %K A188135 nonn,easy,changed %O A188135 0,2 %A A188135 _Paul Curtz_, Mar 30 2011 %E A188135 a(41)-a(47) from _Elmo R. Oliveira_, Oct 19 2024