The On-Line Encyclopedia of Integer Sequences (OEIS)

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A263166

Number of lattice paths starting at {n}^8 and ending when any component equals 0, using steps that decrement one or more components by one.
(history; published version)

#10 by Susanna Cuyler at Sat Apr 25 14:48:13 EDT 2020

STATUS

proposed

approved

#9 by Jean-François Alcover at Sat Apr 25 12:04:38 EDT 2020

STATUS

editing

proposed

#8 by Jean-François Alcover at Sat Apr 25 12:04:34 EDT 2020

MATHEMATICA

g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 8]], {n, 2^8 + 1, 2^9 - 1}];

b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];

a[n_] := b[Table[n, {8}]];

a /@ Range[0, 8] (* Jean-François Alcover, Apr 25 2020, after Alois P. Heinz *)

STATUS

approved

editing

#7 by Alois P. Heinz at Fri Oct 16 10:03:35 EDT 2015

STATUS

editing

approved

#6 by Alois P. Heinz at Fri Oct 16 10:03:32 EDT 2015

LINKS

Alois P. Heinz, <a href="/A263166/b263166.txt">Table of n, a(n) for n = 0..20</a>

STATUS

approved

editing

#5 by Alois P. Heinz at Wed Oct 14 16:00:02 EDT 2015

STATUS

editing

approved

#4 by Alois P. Heinz at Wed Oct 14 15:59:55 EDT 2015

MAPLE

g():= seq(convert(n, base, 2)[1..8], n=257..511):

b:= proc(l) option remember;

`if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))

end:

a:= n-> b([n$8]):

seq(a(n), n=0..8);

STATUS

approved

editing

#3 by Alois P. Heinz at Wed Oct 14 12:19:25 EDT 2015

STATUS

editing

approved

#2 by Alois P. Heinz at Sun Oct 11 13:04:16 EDT 2015

NAME

allocated for Alois P. Heinz

Number of lattice paths starting at {n}^8 and ending when any component equals 0, using steps that decrement one or more components by one.

DATA

1, 255, 277284181, 7671206130046515, 463841686707958609540881, 39946850792952097272345707272335, 4211153593189257990239568354710957472133, 506051495006579137756029271328016744207715324419, 66656513992169790340795231563272399566454175106315563265

OFFSET

0,2

CROSSREFS

Column k=8 of A263159.

KEYWORD

allocated

nonn

AUTHOR

Alois P. Heinz, Oct 11 2015

STATUS

approved

editing

#1 by Alois P. Heinz at Sun Oct 11 12:10:03 EDT 2015

NAME

allocated for Alois P. Heinz

KEYWORD

allocated

STATUS

approved