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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Alois P. Heinz, Antidiagonals n = 0..20, flattened

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

Columns k=0+1, 2-10 give: A000012, A001850, A115866, A263162, A263163, A263164, A263165, A263166, A263167, A263168.

Rows n=0-1 give: A000012, A255047.

Main diagonal gives A263160.

Cf. A210472, A225094, A227578, A227655, A229142, A229345, A262809.

Sequence in context: A081297 A110180 A005765 * A229142 A156535 A243748

Adjacent sequences:  A263156 A263157 A263158 * A263160 A263161 A263162

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Oct 11 2015

STATUS

approved

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Last modified February 24 11:12 EST 2018. Contains 299603 sequences. (Running on oeis4.)