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 A195028 #31 Dec 30 2024 15:18:46 %S A195028 0,27,82,165,276,415,582,777,1000,1251,1530,1837,2172,2535,2926,3345, %T A195028 3792,4267,4770,5301,5860,6447,7062,7705,8376,9075,9802,10557,11340, %U A195028 12151,12990,13857,14752,15675,16626,17605,18612,19647,20710,21801,22920,24067,25242 %N A195028 a(n) = n*(14*n + 13). %C A195028 Sequence found by reading the line from 0, in the direction 0, 27, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. Numbers opposite to the semi-diagonal A195024 in the same square spiral, which is related to the primitive Pythagorean triple [3, 4, 5]. %H A195028 Vincenzo Librandi, <a href="/A195028/b195028.txt">Table of n, a(n) for n = 0..10000</a> %H A195028 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A195028 a(n) = 14*n^2 + 13*n. %F A195028 G.f.: x*(27+x)/(1-x)^3. - _Colin Barker_, Jan 09 2012 %F A195028 From _Elmo R. Oliveira_, Dec 30 2024: (Start) %F A195028 E.g.f.: exp(x)*x*(27 + 14*x). %F A195028 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. (End) %o A195028 (Magma) [14*n^2 +13*n: n in [0..50]]; // _Vincenzo Librandi_, Oct 14 2011 %o A195028 (PARI) a(n)=n*(14*n+13) \\ _Charles R Greathouse IV_, Jun 17 2017 %Y A195028 Cf. A144555, A152760, A185019, A193053, A195019, A195020, A195021, A195023, A195024, A195025, A195026, A195027, A195320, A198017. %K A195028 nonn,easy %O A195028 0,2 %A A195028 _Omar E. Pol_, Oct 13 2011 %E A195028 Name suggested by _Bruno Berselli_, Oct 13 2011