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 A052178 #31 Jan 07 2025 05:57:23
%S A052178 1,12,99,700,4569,28476,172508,1026288,6033690,35195512,204232809,
%T A052178 1181052756,6814746393,39267916380,226097749224,1301403695520,
%U A052178 7490649175326,43123589230824,248351880642630,1430956006648056,8249467230853002,47587180659332248
%N A052178 Number of walks of length n on the simple cubic lattice terminating at height 2 above the (x,y)-plane.
%H A052178 Rigoberto Flórez, Leandro Junes, and José L. Ramírez, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL21/Florez/florez4.html">Further Results on Paths in an n-Dimensional Cubic Lattice</a>, Journal of Integer Sequences, Vol. 21 (2018), Article 18.1.2.
%H A052178 R. K. Guy, <a href="https://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.
%p A052178 b:= proc(n, k) option remember; `if`(min(n, k)<0, 0,
%p A052178 `if`(max(n, k)=0, 1, b(n-1, k-1)+4*b(n-1, k)+b(n-1, k+1)))
%p A052178 end:
%p A052178 a:= n-> b(n, 2):
%p A052178 seq(a(n), n=2..25); # _Alois P. Heinz_, Oct 28 2021
%t A052178 b[n_, k_] := b[n, k] = If[Min[n, k] < 0, 0, If[Max[n, k] == 0, 1, b[n - 1, k - 1] + 4*b[n - 1, k] + b[n - 1, k + 1]]];
%t A052178 a[n_] := b[n, 2];
%t A052178 Table[a[n], {n, 2, 25}] (* _Jean-François Alcover_, Jan 07 2025, after _Alois P. Heinz_ *)
%Y A052178 Column 2 of A052179.
%K A052178 nonn,walk
%O A052178 2,2
%A A052178 _N. J. A. Sloane_, Jan 26 2000
%E A052178 More terms and title improved by _Sean A. Irvine_, Oct 28 2021