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A026725 Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1<=k<=n-1, T(n,k)=T(n-1,k-1)+T(n-2,k-1)+T(n-1,k) if n is odd and k=(n-1)/2, else T(n,k)=T(n-1,k-1)+T(n-1,k). 26

%I

%S 1,1,1,1,2,1,1,4,3,1,1,5,7,4,1,1,6,16,11,5,1,1,7,22,27,16,6,1,1,8,29,

%T 65,43,22,7,1,1,9,37,94,108,65,29,8,1,1,10,46,131,267,173,94,37,9,1,1,

%U 11,56,177,398,440,267,131,46,10,1,1,12,67,233

%N Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1<=k<=n-1, T(n,k)=T(n-1,k-1)+T(n-2,k-1)+T(n-1,k) if n is odd and k=(n-1)/2, else T(n,k)=T(n-1,k-1)+T(n-1,k).

%C T(n+2,n) = A134869(n+1). - _Philippe Deléham_, Feb 01 2014

%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 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, i+1)-to-(i+1, i+2) for i >= 0.

%F Comment from _Rick L. Shepherd_, Aug 05 2002: Probably this should be changed to "and edges (i+1, i)-to-(i+2, i+1) for i >= 0."

%e Triangle begins:

%e 1

%e 1 1

%e 1 2 1

%e 1 4 3 1

%e 1 5 7 4 1

%e 1 6 16 11 5 1

%e 1 7 22 27 16 6 1

%e 1 8 29 65 43 22 7 1

%e 1 9 37 94 108 65 29 8 1

%e 1 10 46 131 267 173 94 37 9 1

%e 1 11 56 177 398 440 267 131 46 10 1

%e 1 12 67 233 575 1105 707 398 177 56 11 1

%e ... - _Philippe Deléham_, Feb 01 2014

%Y Cf. A026674.

%K nonn,tabl

%O 1,5

%A _Clark Kimberling_

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Last modified December 10 20:55 EST 2018. Contains 318049 sequences. (Running on oeis4.)