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 A318943 #17 May 24 2024 16:02:26
%S A318943 0,0,0,1,6,21,68,208,612,1752,4916,13588,37128,100548,270404,723208,
%T A318943 1925844,5110644,13524872,35713828,94140900,247806600,651572660,
%U A318943 1711695508,4493475336,11789439876,30917835908,81053196808,212426303892,556607396532
%N A318943 Number of Dyck paths with n nodes and altitude 3.
%H A318943 Colin Barker, <a href="/A318943/b318943.txt">Table of n, a(n) for n = 0..1000</a>
%H A318943 E. Czabarka et al, <a href="https://doi.org/10.1016/j.disc.2018.06.032">Enumerations of peaks and valleys on non-decreasing Dyck paths</a>, Disc. Math. 341 (2018) 2789-2807.
%H A318943 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-17,16,-4).
%F A318943 a(n) = 8*A001906(n+1)-20*A001906(n)-2^(n-5)*(16+3*n), n>=4. - _R. J. Mathar_, Apr 09 2019
%F A318943 a(n) = 7*a(n-1) - 17*a(n-2) + 16*a(n-3) - 4*a(n-4) for n>7. - _Colin Barker_, Apr 11 2019
%p A318943 (1-x)^2*x^3*(1+x-3*x^2)/(1-2*x)^2/(1-3*x+x^2) ;
%p A318943 taylor(%,x=0,30) ;
%p A318943 gfun[seriestolist](%) ; # _R. J. Mathar_, Nov 25 2018
%t A318943 LinearRecurrence[{7, -17, 16, -4}, {0, 0, 0, 1, 6, 21, 68, 208}, 50] (* _Paolo Xausa_, May 24 2024 *)
%o A318943 (PARI) concat([0,0,0], Vec(x^3*(1 - x)^2*(1 + x - 3*x^2) / ((1 - 2*x)^2*(1 - 3*x + x^2)) + O(x^40))) \\ _Colin Barker_, Apr 11 2019
%Y A318943 A column of A318942.
%K A318943 nonn,easy
%O A318943 0,5
%A A318943 _N. J. A. Sloane_, Sep 18 2018