|
|
A276852
|
|
Number of positive walks with n steps {-3,-2,-1,1,2,3} starting at the origin, ending at altitude 1, and staying strictly above the x-axis.
|
|
15
|
|
|
0, 1, 2, 7, 28, 121, 560, 2677, 13230, 66742, 343092, 1788681, 9439870, 50321865, 270594896, 1465941763, 7993664588, 43839212778, 241650560756, 1338084935826, 7439615051328, 41516113036777, 232452845782308, 1305500166481715, 7352433083806020, 41514430735834714
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
MATHEMATICA
|
walks[n_, k_, h_] = 0;
walks[1, k_, h_] := Boole[0 < k <= h];
walks[n_, k_, h_] /; n >= 2 && k > 0 := walks[n, k, h] = Sum[walks[n - 1, k - x, h], {x, h}] + Sum[walks[n - 1, k + x, h], {x, h}];
(* walks represents the number of positive walks with n steps {-h, -h+1, ... -1, 1, ..., h} that end at altitude k *)
A276852[n_] := (Do[walks[m, k, 3], {m, n}, {k, 3 m}]; walks[n, 1, 3]) (* Davin Park, Oct 10 2016 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,walk
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|