

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,n1) = n+1; for n >= 2, T(n,k) = T(n1,k1) + T(n2,k1) + T(n1,k) if n is even and k = n/2, else T(n,k) = T(n1,k1) + T(n1,k).


17



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, 65, 65, 29, 8, 1, 1, 9, 37, 94, 173, 94, 37, 9, 1, 1, 10, 46, 131, 267, 267, 131, 46, 10, 1, 1, 11, 56, 177, 398, 707, 398, 177, 56, 11, 1, 1, 12, 67
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OFFSET

0,5


LINKS



FORMULA

T(n, k) = number of paths from (0, 0) to (nk, 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.


EXAMPLE

E.g., 11 = T(4, 2) = T(3, 1) + T(2, 2) + T(3, 2) = 4 + 3 + 4.
Triangle begins:
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 65 65 29 8 1
1 9 37 94 173 94 37 9 1
1 10 46 131 267 267 131 46 10 1
1 11 56 177 398 707 398 177 56 11 1
1 12 67 233 575 1105 1105 575 233 67 12 1


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS

Formula corrected by David Perkinson (davidp(AT)reed.edu), Sep 19 2001 and also by Rob Arthan, Jan 16 2003


STATUS

approved



