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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. 9
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, 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, 127, 129, 86, 34, 12, 7, 1, 1, 10, 45, 120, 211, 256, 215, 120, 46, 19, 8, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..77.

MATHEMATICA

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];

Table[T[h - k, k], {h, 0, 11}, {k, h, 0, -1}]  // Flatten (* Jean-Fran├žois Alcover, Mar 06 2019 *)

CROSSREFS

Cf. A047089 (with y=x/2), A047100 (with y=x/3).

Sequence in context: A208891 A177767 A047030 * A096751 A293551 A099233

Adjacent sequences:  A047117 A047118 A047119 * A047121 A047122 A047123

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified November 29 18:41 EST 2021. Contains 349416 sequences. (Running on oeis4.)