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 A005905 M5001 #42 Nov 29 2024 17:40:39
%S A005905 1,16,58,128,226,352,506,688,898,1136,1402,1696,2018,2368,2746,3152,
%T A005905 3586,4048,4538,5056,5602,6176,6778,7408,8066,8752,9466,10208,10978,
%U A005905 11776,12602,13456,14338,15248,16186,17152,18146,19168,20218,21296,22402,23536,24698
%N A005905 Number of points on surface of truncated tetrahedron: a(n) = 14*n^2 + 2 for n > 0, a(0)=1.
%C A005905 Also sequence found by reading the segment (1,16) together with the line from 16, in the direction 16, 58, ... , in the square spiral whose vertices are the generalized enneagonal numbers A118277. - _Omar E. Pol_, Nov 05 2012
%D A005905 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005905 H. S. M. Coxeter, <a href="http://dx.doi.org/10.1007/978-94-010-2115-9_4">Polyhedral Numbers</a>, in R. S. Cohen et al., editors, For Dirk Struik. Reidel, Dordrecht, 1974, pp. 25-35.
%H A005905 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 A005905 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.
%H A005905 B. K. Teo and N. J. A. Sloane, <a href="http://neilsloane.com/doc/magic1/magic1.html">Magic numbers in polygonal and polyhedral clusters</a>, Inorgan. Chem., Vol. 24 (1985), pp. 4545-4558.
%H A005905 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A005905 From _Elmo R. Oliveira_, Nov 29 2024: (Start)
%F A005905 G.f.: (1 + x)*(1 + 12*x + x^2)/(1-x)^3.
%F A005905 E.g.f.: 2*exp(x)*(7*x^2 + 7*x + 1) - 1.
%F A005905 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 4. (End)
%p A005905 A005905:=-(z+1)*(z**2+12*z+1)/(z-1)**3; # [_Simon Plouffe_ in his 1992 dissertation.]
%t A005905 a[0] = 1; a[n_] := 14 n^2 + 2; Table[a[n], {n, 0, 50}] (* _Wesley Ivan Hurt_, Mar 04 2014 *)
%o A005905 (PARI) a(n) = if (n==0, 1, 14*n^2+2); \\ _Michel Marcus_, Mar 04 2014
%Y A005905 Cf. A118277, A206399.
%K A005905 nonn,easy
%O A005905 0,2
%A A005905 _N. J. A. Sloane_
%E A005905 More terms from _Michel Marcus_, Mar 04 2014