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 A005570 M5038 #72 Jan 28 2025 15:28:27
%S A005570 17,50,99,164,245,342,455,584,729,890,1067,1260,1469,1694,1935,2192,
%T A005570 2465,2754,3059,3380,3717,4070,4439,4824,5225,5642,6075,6524,6989,
%U A005570 7470,7967,8480,9009,9554,10115,10692,11285,11894,12519,13160,13817,14490,15179,15884,16605
%N A005570 Number of walks on cubic lattice.
%C A005570 Partial sums of A158057.
%D A005570 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005570 Jeremy Gardiner, <a href="/A005570/b005570.txt">Table of n, a(n) for n = 1..999</a>
%H A005570 Richard K. Guy, <a href="/A005555/a005555.pdf">Letter to N. J. A. Sloane, May 1990</a>.
%H A005570 Richard K. Guy, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/GUY/catwalks.html">Catwalks, sandsteps and Pascal pyramids</a>, J. Integer Sequences, Vol. 3 (2000), Article 00.1.6 (see figure 7).
%H A005570 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A005570 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.
%H A005570 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A005570 a(n) = 8*n^2 + 9*n.
%F A005570 G.f.: (17-x)/(1-x)^3. _Simon Plouffe_ in his 1992 dissertation.
%F A005570 a(n) = 16*A000217(n) + n. - _Jon Perry_, Nov 05 2014
%F A005570 Sum_{n>=1} 1/a(n) = 80/81 +Psi(1/8)/9+gamma/9 = 0.11973.. see A001620 and A250129. - _R. J. Mathar_, May 30 2022
%F A005570 Sum_{n>=1} 1/a(n) = 80/81 - (sqrt(2)+1)*Pi/18 - log(1+sqrt(2))*sqrt(2)/9 -4*log(2)/9. - _Amiram Eldar_, Sep 10 2022
%F A005570 From _Elmo R. Oliveira_, Jan 28 2025: (Start)
%F A005570 E.g.f.: exp(x)*x*(17 + 8*x).
%F A005570 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%t A005570 CoefficientList[Series[(17 - x) / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Nov 05 2014 *)
%o A005570 (PARI) Vec((17-x)/(1-x)^3 + O(x^50)) \\ _Michel Marcus_, Nov 05 2014
%o A005570 (Magma) [8*n^2 + 9*n : n in [1..40]]; // _Vincenzo Librandi_, Nov 05 2014
%Y A005570 Cf. A000217, A001620, A158057, A250129.
%K A005570 nonn,walk,easy
%O A005570 1,1
%A A005570 _N. J. A. Sloane_
%E A005570 Formula and more terms from _Jeffrey Shallit_, Aug 15 1995