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 A068913 #33 Mar 31 2024 02:07:24
%S A068913 1,0,1,0,2,1,0,2,2,1,0,4,4,2,1,0,4,6,4,2,1,0,8,12,8,4,2,1,0,8,18,14,8,
%T A068913 4,2,1,0,16,36,28,16,8,4,2,1,0,16,54,48,30,16,8,4,2,1,0,32,108,96,60,
%U A068913 32,16,8,4,2,1,0,32,162,164,110,62,32,16,8,4,2,1,0,64,324,328,220,124,64,32,16,8,4,2,1
%N A068913 Square array read by antidiagonals of number of k step walks (each step +-1 starting from 0) which are never more than n or less than -n.
%H A068913 Alois P. Heinz, <a href="/A068913/b068913.txt">Antidiagonals n = 0..200, flattened</a>
%F A068913 Starting with T(n, 0) = 1, if (k-n) is negative or even then T(n, k) = 2*T(n, k-1), otherwise T(n, k) = 2*T(n, k-1) - A061897(n+1, (k-n-1)/2). So for n>=k, T(n, k) = 2^k. [Corrected by _Sean A. Irvine_, Mar 23 2024]
%F A068913 T(n,0) = 1, T(n,k) = (2^k/(n+1))*Sum_{r=1..n+1} (-1)^r*cos((Pi*(2*r-1))/(2*(n+1)))^k*cot((Pi*(1-2*r))/(4*(n+1))). - _Herbert Kociemba_, Sep 23 2020
%e A068913 Rows start:
%e A068913 1, 0, 0, 0, 0, ...
%e A068913 1, 2, 2, 4, 4, ...
%e A068913 1, 2, 4, 6, 12, ...
%e A068913 1, 2, 4, 8, 14, ...
%e A068913 ...
%t A068913 T[n_,0]=1; T[n_,k_]:=2^k/(n+1) Sum[(-1)^r Cos[(Pi (2r-1))/(2 (n+1))]^k Cot[(Pi (1-2r))/(4 (n+1))],{r,1,n+1}]; Table[T[r,n-r],{n,0,20},{r,0,n}]//Round//Flatten (* _Herbert Kociemba_, Sep 23 2020 *)
%Y A068913 Cf. early rows: A000007, A016116 (without initial term), A068911, A068912, A216212, A216241, A235701.
%Y A068913 Central and lower diagonals are A000079, higher diagonals include A000918, A028399.
%K A068913 nonn,tabl
%O A068913 0,5
%A A068913 _Henry Bottomley_, Mar 06 2002