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A263165
Number of lattice paths starting at {n}^7 and ending when any component equals 0, using steps that decrement one or more components by one.
2
1, 127, 11917837, 15302345348179, 38074918201135688881, 127994492508527577494290807, 511210318493877135287739912958933, 2283244029676857615289372083169016508547, 11029283913008516141643899112236047179180872449
OFFSET
0,2
LINKS
MAPLE
g():= seq(convert(n, base, 2)[1..7], n=129..255):
b:= proc(l) option remember;
`if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
end:
a:= n-> b([n$7]):
seq(a(n), n=0..9);
MATHEMATICA
g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 7]], {n, 2^7 + 1, 2^8 - 1}];
b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
a[n_] := b[Table[n, {7}]];
a /@ Range[0, 9] (* Jean-François Alcover, Apr 25 2020, after Alois P. Heinz *)
CROSSREFS
Column k=7 of A263159.
Sequence in context: A334668 A135813 A112016 * A135982 A135983 A101327
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 11 2015
STATUS
approved