A026670 - OEIS

%I #26 Oct 25 2019 16:55:38

%S 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 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 1,11,56,177,398,707,398,177,56,11,1,1,12,67

%N 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 Rob Arthan, <a href="/A026674/a026674.txt">Comments on A026674, A026725, A026670</a>

%F 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 E.g., 11 = T(4, 2) = T(3, 1) + T(2, 2) + T(3, 2) = 4 + 3 + 4.

%e Triangle begins:

%e 1

%e 1  1

%e 1  3  1

%e 1  4  4   1

%e 1  5 11   5   1

%e 1  6 16  16   6    1

%e 1  7 22  43  22    7    1

%e 1  8 29  65  65   29    8   1

%e 1  9 37  94 173   94   37   9   1

%e 1 10 46 131 267  267  131  46  10  1

%e 1 11 56 177 398  707  398 177  56 11  1

%e 1 12 67 233 575 1105 1105 575 233 67 12 1

%e ... - _Philippe Deléham_, Feb 02 2014

%Y Cf. A026674.

%K nonn,tabl

%O 0,5

%A _Clark Kimberling_

%E Formula corrected by David Perkinson (davidp(AT)reed.edu), Sep 19 2001 and also by _Rob Arthan_, Jan 16 2003

%E Typo in name corrected by _Sean A. Irvine_, Oct 09 2019

%E Offset corrected by _R. J. Mathar_ and _Sean A. Irvine_, Oct 25 2019