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A263159 revision #10

A263159
Number A(n,k) of lattice paths starting at {n}^k and ending when k or any component equals 0, using steps that decrement one or more components by one; square array A(n,k), n>=0, k>=0, read by antidiagonals.
19
1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 7, 13, 1, 1, 1, 15, 157, 63, 1, 1, 1, 31, 2101, 5419, 321, 1, 1, 1, 63, 32461, 717795, 220561, 1683, 1, 1, 1, 127, 580693, 142090291, 328504401, 9763807, 8989, 1, 1, 1, 255, 11917837, 39991899123, 944362553521, 172924236255, 454635973, 48639, 1, 1
OFFSET
0,8
LINKS
EXAMPLE
1, 1, 1, 1, 1, 1, ...
1, 1, 3, 7, 15, 31, ...
1, 1, 13, 157, 2101, 32461, ...
1, 1, 63, 5419, 717795, 142090291, ...
1, 1, 321, 220561, 328504401, 944362553521, ...
1, 1, 1683, 9763807, 172924236255, 7622403922836151, ...
MAPLE
s:= proc(n) option remember; `if`(n=0, {[]},
map(x-> [[x[], 0], [x[], 1]][], s(n-1)))
end:
b:= proc(l) option remember; `if`(l=[] or l[1]=0, 1,
add((p-> `if`(p[1]<0, 0, `if`(p[1]=0, 1, b(p)))
)(sort(l-x)), x=s(nops(l)) minus {[0$nops(l)]}))
end:
A:= (n, k)-> b([n$k]):
seq(seq(A(n, d-n), n=0..d), d=0..10);
CROSSREFS
Rows n=0-1 give: A000012, A255047.
Main diagonal gives A263160.
Sequence in context: A005765 A360289 A343717 * A229142 A156535 A365427
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Oct 11 2015
STATUS
editing