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 A081589 #15 Jun 09 2025 00:40:48
%S A081589 1,13,61,145,265,421,613,841,1105,1405,1741,2113,2521,2965,3445,3961,
%T A081589 4513,5101,5725,6385,7081,7813,8581,9385,10225,11101,12013,12961,
%U A081589 13945,14965,16021,17113,18241,19405,20605,21841,23113,24421,25765,27145,28561,30013,31501
%N A081589 Third row of Pascal-(1,5,1) array A081580.
%H A081589 Vincenzo Librandi, <a href="/A081589/b081589.txt">Table of n, a(n) for n = 0..1000</a>
%H A081589 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A081589 a(n) = 1 - 6*n + 18*n^2.
%F A081589 G.f.: (1+5*x)^2/(1-x)^3.
%F A081589 From _Elmo R. Oliveira_, Jun 06 2025: (Start)
%F A081589 E.g.f.: exp(x)*(1 + 12*x + 18*x^2).
%F A081589 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%t A081589 CoefficientList[Series[(1 + 5 x)^2 / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 09 2013 *)
%o A081589 (Magma) [1-6*n+18*n^2: n in [0..40]]; // _Vincenzo Librandi_, Aug 09 2013
%o A081589 (PARI) a(n)=18*n^2-6*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A081589 Cf. A016921, A081580, A081590.
%K A081589 easy,nonn
%O A081589 0,2
%A A081589 _Paul Barry_, Mar 23 2003