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A047120 Array T 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 touches the line y=x/4 only at lattice points.

%I A047120 #14 Mar 06 2019 02:50:03
%S A047120 1,1,1,1,1,1,1,2,1,1,1,3,3,1,1,1,4,6,4,2,1,1,5,10,10,6,3,1,1,6,15,20,
%T A047120 16,6,4,1,1,7,21,35,36,22,6,5,1,1,8,28,56,71,58,28,6,6,1,1,9,36,84,
%U A047120 127,129,86,34,12,7,1,1,10,45,120,211,256,215,120,46,19,8,1
%N A047120 Array T 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 touches the line y=x/4 only at lattice points.
%t A047120 T[_, 0] = 1; T[0, _] = 1; T[h_, k_] := T[h, k] = If[k-1 >= h/4 || k <= h/4, T[h, k-1], 0] + T[h-1, k];
%t A047120 Table[T[h - k, k], {h, 0, 11}, {k, h, 0, -1}]  // Flatten (* _Jean-François Alcover_, Mar 06 2019 *)
%Y A047120 Cf. A047089 (with y=x/2), A047100 (with y=x/3).
%K A047120 nonn,tabl
%O A047120 0,8
%A A047120 _Clark Kimberling_