

A047110


Array read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right and no upstep crosses the line y=2x/3. (Thus a path crosses the line only at lattice points and on rightsteps.).


17



1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 1, 4, 5, 5, 4, 1, 1, 5, 9, 10, 9, 5, 1, 1, 6, 14, 19, 10, 14, 6, 1, 1, 7, 20, 33, 29, 24, 20, 7, 1, 1, 8, 27, 53, 62, 29, 44, 27, 8, 1, 1, 9, 35, 80, 115, 91, 73, 71, 35, 9, 1, 1, 10, 44, 115, 195, 206, 164, 144, 106, 44, 10, 1
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OFFSET

0,8


COMMENTS

T is the transpose of the array in A125778.


LINKS

Alois P. Heinz, Antidiagonals n = 0..140, flattened


EXAMPLE

Diagonals (beginning on row 0): {1}; {1,1}; {1,1,1}; {1,2,2,1};...


MAPLE

T:= proc(h, k) option remember;
`if`([h, k]=[0, 0], 1, `if`(h<0 or k<0, 0, T(h1, k)+
`if`(3*k>2*h and 3*(k1)<2*h, 0, T(h, k1))))
end:
seq(seq(T(h, dh), h=0..d), d=0..20); # Alois P. Heinz, Apr 04 2012


MATHEMATICA

T[h_, k_] := T[h, k] = If[{h, k} == {0, 0}, 1, If[h<0  k<0, 0, T[h1, k]+If[3*k > 2*h && 3*(k1) < 2*h, 0, T[h, k1]]]]; Table[Table[T[h, dh], {h, 0, d}], {d, 0, 20}] // Flatten (* JeanFrançois Alcover, Mar 03 2014, after Alois P. Heinz *)


CROSSREFS

Cf. A125778.
Sequence in context: A050176 A047130 A125778 * A288533 A093869 A329870
Adjacent sequences: A047107 A047108 A047109 * A047111 A047112 A047113


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling. Definition revised Dec 08 2006


STATUS

approved



