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 A026747 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 even and 1<=k<=n/2, else T(n,k)=T(n-1,k-1)+T(n-1,k). 30
 1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 6, 11, 5, 1, 1, 7, 17, 16, 6, 1, 1, 9, 30, 44, 22, 7, 1, 1, 10, 39, 74, 66, 29, 8, 1, 1, 12, 58, 143, 184, 95, 37, 9, 1, 1, 13, 70, 201, 327, 279, 132, 46, 10, 1, 1, 15, 95, 329, 671, 790, 411, 178, 56, 11, 1, 1, 16 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS FORMULA 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, 2h+i)-to-(i+1, 2h+i+1) for i >= 0, h>=0. EXAMPLE 1; 1,  1; 1,  3,  1; 1,  4,  4,  1; 1,  6, 11,  5,  1; 1,  7, 17, 16,  6,  1; 1,  9, 30, 44, 22,  7,  1; MAPLE A026747 := proc(n, k)     if k=0 or k = n then         1;     elif type(n, 'even') and k <= n/2 then         procname(n-1, k-1)+procname(n-2, k-1)+procname(n-1, k) ;     else         procname(n-1, k-1)+procname(n-1, k) ;     end if ; end proc: # R. J. Mathar, Jun 30 2013 CROSSREFS Cf. A026754 (row sums). Sequence in context: A026626 A136482 A026648 * A026374 A174032 A180979 Adjacent sequences:  A026744 A026745 A026746 * A026748 A026749 A026750 KEYWORD nonn,tabl AUTHOR STATUS approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)