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 A081270 #27 Nov 13 2024 17:12:33
%S A081270 3,16,38,69,109,158,216,283,359,444,538,641,753,874,1004,1143,1291,
%T A081270 1448,1614,1789,1973,2166,2368,2579,2799,3028,3266,3513,3769,4034,
%U A081270 4308,4591,4883,5184,5494,5813,6141,6478,6824,7179,7543,7916,8298,8689,9089,9498,9916
%N A081270 Diagonal of triangular spiral in A051682.
%H A081270 Vincenzo Librandi, <a href="/A081270/b081270.txt">Table of n, a(n) for n = 0..1000</a>
%H A081270 Hacène Belbachir, Toufik Djellal, Jean-Gabriel Luque, <a href="https://arxiv.org/abs/1703.00323">On the self-convolution of generalized Fibonacci numbers</a>, arXiv:1703.00323 [math.CO], 2017.
%H A081270 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A081270 a(n) = A064226(n) + 2*n.
%F A081270 a(n) = 3*binomial(n,0) + 13*binomial(n,1) + 9*binomial(n,2); binomial transform of (3, 13, 9, 0, 0, 0, ...).
%F A081270 a(n) = (9*n^2 + 17*n + 6)/2.
%F A081270 G.f.: (3 + 7*x - x^2)/(1-x)^3.
%F A081270 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Jul 08 2012
%F A081270 E.g.f.: exp(x)*(6 + 26*x + 9*x^2)/2. - _Elmo R. Oliveira_, Nov 13 2024
%t A081270 CoefficientList[Series[(3+7x-x^2)/(1-x)^3,{x,0,50}],x] (* _Vincenzo Librandi_, Jul 08 2012 *)
%o A081270 (Magma) [(9*n^2+17*n+6)/2: n in [0..50]]; // _Vincenzo Librandi_, Jul 08 2012
%o A081270 (PARI) a(n)=(9*n^2+17*n+6)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A081270 Cf. A064226, A081268.
%K A081270 easy,nonn
%O A081270 0,1
%A A081270 _Paul Barry_, Mar 15 2003