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 A081271 #27 Aug 30 2025 15:45:27
%S A081271 1,13,34,64,103,151,208,274,349,433,526,628,739,859,988,1126,1273,
%T A081271 1429,1594,1768,1951,2143,2344,2554,2773,3001,3238,3484,3739,4003,
%U A081271 4276,4558,4849,5149,5458,5776,6103,6439,6784,7138,7501,7873,8254,8644,9043,9451
%N A081271 Vertical of triangular spiral in A051682.
%C A081271 Lies to the right of the y-axis of the triangle.
%C A081271 Binomial transform of (1, 12, 9, 0, 0, 0, ...).
%H A081271 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A081271 G.f.: (1 + 10*x - 2*x^2)/(1 - x)^3.
%F A081271 a(n) = binomial(n,0) + 12*binomial(n,1) + 9*binomial(n,2).
%F A081271 a(n) = (9*n^2 + 15*n + 2)/2.
%F A081271 a(0) = 1, a(n) = a(n-1) + 9*n + 3 for n > 0 - _Gerald McGarvey_, Aug 18 2004
%F A081271 From _Elmo R. Oliveira_, Oct 25 2024: (Start)
%F A081271 E.g.f.: exp(x)*(1 + 12*x + 9*x^2/2).
%F A081271 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A081271 LinearRecurrence[{3,-3,1},{1,13,34},50] (* _Harvey P. Dale_, Aug 30 2025 *)
%o A081271 (PARI) a(n)=(9*n^2+15*n+2)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A081271 Cf. A062741, A283394 (see Crossrefs section).
%K A081271 nonn,easy,changed
%O A081271 0,2
%A A081271 _Paul Barry_, Mar 15 2003