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 A026670 #26 Oct 25 2019 16:55:38 %S A026670 1,1,1,1,3,1,1,4,4,1,1,5,11,5,1,1,6,16,16,6,1,1,7,22,43,22,7,1,1,8,29, %T A026670 65,65,29,8,1,1,9,37,94,173,94,37,9,1,1,10,46,131,267,267,131,46,10,1, %U A026670 1,11,56,177,398,707,398,177,56,11,1,1,12,67 %N A026670 Triangular array T read by rows: T(n,0) = T(n,n) = 1 for n >= 0; for n >= 1, T(n,1) = T(n,n-1) = n+1; for n >= 2, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if n is even and k = n/2, else T(n,k) = T(n-1,k-1) + T(n-1,k). %H A026670 Rob Arthan, <a href="/A026674/a026674.txt">Comments on A026674, A026725, A026670</a> %F A026670 T(n, k) = number of paths from (0, 0) to (n-k, k) in the directed graph having vertices (i, j) and edges (i, j)-to-(i+1, j) and (i, j)-to-(i, j+1) for i, j >= 0 and edges (i, j)-to-(i+1, j+1) for i=j. %e A026670 E.g., 11 = T(4, 2) = T(3, 1) + T(2, 2) + T(3, 2) = 4 + 3 + 4. %e A026670 Triangle begins: %e A026670 1 %e A026670 1 1 %e A026670 1 3 1 %e A026670 1 4 4 1 %e A026670 1 5 11 5 1 %e A026670 1 6 16 16 6 1 %e A026670 1 7 22 43 22 7 1 %e A026670 1 8 29 65 65 29 8 1 %e A026670 1 9 37 94 173 94 37 9 1 %e A026670 1 10 46 131 267 267 131 46 10 1 %e A026670 1 11 56 177 398 707 398 177 56 11 1 %e A026670 1 12 67 233 575 1105 1105 575 233 67 12 1 %e A026670 ... - _Philippe Deléham_, Feb 02 2014 %Y A026670 Cf. A026674. %K A026670 nonn,tabl %O A026670 0,5 %A A026670 _Clark Kimberling_ %E A026670 Formula corrected by David Perkinson (davidp(AT)reed.edu), Sep 19 2001 and also by _Rob Arthan_, Jan 16 2003 %E A026670 Typo in name corrected by _Sean A. Irvine_, Oct 09 2019 %E A026670 Offset corrected by _R. J. Mathar_ and _Sean A. Irvine_, Oct 25 2019