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A190425 Number of one-sided prudent walks from (0,0) to (n,n), with floor(n/2)+n east steps, floor(n/2) west steps and n north steps. 1
1, 2, 12, 60, 700, 3780, 51744, 288288, 4247100, 24066900, 369881512, 2118412296, 33466634656, 193076738400, 3109838832000, 18037065225600, 294718130342460, 1716299700229620, 28355714001615000, 165657066009435000, 2761067350729888200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

S. Gao, H. Niederhausen, Sequences Arising From Prudent Self-Avoiding Walks (submitted to INTEGERS: The Electronic Journal of Combinatorial Number Theory).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

MAPLE

a:= n-> b(0, iquo(n, 2), n, iquo(n, 2)+n):

b:= proc(i, w, no, e) option remember; `if`(-1 in {w, no, e}, 0,

      `if`(no=0 and w=0 and e=0, 1,  b(0, w, no-1, e)+

      `if`(i<1, b(-1, w-1, no, e), 0)+`if`(i>-1, b(1, w, no, e-1), 0)))

    end:

seq(a(n), n=0..20); # Alois P. Heinz, Jun 04 2011

MATHEMATICA

a[n_] := b[0, Quotient[n, 2], n, Quotient[n, 2] + n]; b[i_, w_, no_, e_] := b[i, w, no, e] = If[MemberQ[{w, no, e}, -1], 0, If[no == 0 && w == 0 && e == 0, 1, b[0, w, no - 1, e] + If[i < 1, b[-1, w - 1, no, e], 0] + If[i > -1, b[1, w, no, e - 1], 0]]]; Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Oct 24 2016, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A074445 A038154 A061834 * A145630 A082688 A099996

Adjacent sequences:  A190422 A190423 A190424 * A190426 A190427 A190428

KEYWORD

nonn,walk

AUTHOR

Shanzhen Gao, May 10 2011

EXTENSIONS

More terms from Alois P. Heinz, Jun 04 2011

STATUS

approved

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Last modified April 20 16:17 EDT 2019. Contains 322310 sequences. (Running on oeis4.)