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 A153793 #27 Sep 08 2022 08:45:40 %S A153793 0,13,65,156,286,455,663,910,1196,1521,1885,2288,2730,3211,3731,4290, %T A153793 4888,5525,6201,6916,7670,8463,9295,10166,11076,12025,13013,14040, %U A153793 15106,16211,17355,18538,19760,21021,22321,23660,25038,26455 %N A153793 13 times pentagonal numbers: a(n) = 13*n*(3*n-1)/2. %H A153793 Ivan Panchenko, <a href="/A153793/b153793.txt">Table of n, a(n) for n = 0..1000</a> %H A153793 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A153793 a(n) = (39*n^2 - 13*n)/2 = 13*A000326(n). %F A153793 a(n) = 39*n + a(n-1) - 26 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010 %F A153793 G.f.: 13*x*(1 + 2*x)/(1-x)^3. - _Colin Barker_, Feb 14 2012 %F A153793 From _G. C. Greubel_, Aug 29 2016: (Start) %F A153793 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. %F A153793 E.g.f.: (13/2)*x*(2+3*x)*exp(x). (End) %p A153793 A153793:=n->13*n*(3*n-1)/2: seq(A153793(n), n=0..60); # _Wesley Ivan Hurt_, Aug 29 2016 %t A153793 Table[13*n*(3*n-1)/2, {n,0,25}] (* or *) LinearRecurrence[{3,-3,1}, {0,13,65}, 25] (* _G. C. Greubel_, Aug 29 2016 *) %t A153793 13*PolygonalNumber[5,Range[0,40]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 16 2016 *) %o A153793 (PARI) a(n) = (39*n^2 - 13*n)/2; \\ _Altug Alkan_, Aug 29 2016 %o A153793 (Magma) [13*n*(3*n-1)/2: n in [0..60]]; // _Wesley Ivan Hurt_, Aug 29 2016 %Y A153793 Cf. A000326, A153792. %K A153793 nonn,easy %O A153793 0,2 %A A153793 _Omar E. Pol_, Jan 01 2009