STATUS
editing
proposed
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Revisions by Jean-François Alcover
(See also Jean-François Alcover's wiki page)(Bold, blue-underlined text is an addition; faded, red-underlined text is a
Showing entries 1-10 | older changes
MATHEMATICA
b[x_, y_] := b[x, y] = If[x == 0, If[y == 0, 1, 0],
If[y > 1, b[x - 1, 0], 0] + b[x - 1, Abs[y - 1]] + b[x - 1, y + 1]];
a[n_] := b[n, 0];
Table[a[n], {n, 0, 32}] (* Jean-François Alcover, Feb 23 2025, after Alois P. Heinz *)
STATUS
approved
editing
Number of Dyck bridges with resets from any height to zero from (0,0) to (n,0).
(history; published version)
(history; published version)
STATUS
editing
proposed
MATHEMATICA
b[x_, y_] := b[x, y] = If[x == 0, If[y == 0, 1, 0],
b[x - 1, 0] + b[x - 1, Abs[y - 1]] + b[x - 1, y + 1]];
a[n_] := b[n, 0];
Table[a[n], {n, 0, 32}] (* Jean-François Alcover, Feb 22 2025, after Alois P. Heinz *)
STATUS
approved
editing
STATUS
editing
proposed
MATHEMATICA
s[n_] := s[n] = If[n == 0, 0, s[n - 1] + 1/(n*b[n])];
b[n_] := b[n] = 1 + Floor[1/((1 - s[n - 1])*n)];
a[n_] := If[n == 0, 1, Denominator[s[n]]/LCM @@ Range[n]];
Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Feb 14 2025, after Alois P. Heinz *)
STATUS
approved
editing
STATUS
editing
proposed
MATHEMATICA
s[n_] := s[n] = If[n == 0, 0, s[n - 1] + 1/(n*b[n])];
b[n_] := b[n] = 1 + Floor[1/((1 - s[n - 1])*n)];
a[n_] := Denominator[s[n + 1]] - Denominator[s[n]];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Feb 14 2025, after Alois P. Heinz *)
STATUS
approved
editing
STATUS
editing
proposed
STATUS
editing
proposed