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A263162 Number of lattice paths starting at {n}^4 and ending when any component equals 0, using steps that decrement one or more components by one. 2
1, 15, 2101, 717795, 328504401, 172924236255, 98788351385893, 59547100211425779, 37279994808479614465, 24006888102075722880975, 15800133137207909144690421, 10580854797781352259168325347, 7186571606168294602440625922385, 4938826696886704892539811529645855 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..263 (terms 0..170 from Alois P. Heinz)

FORMULA

a(n) ~ c * d^n / (Pi^(3/2) * n^(3/2)), where d = 195 + 138*sqrt(2) + 4*sqrt(4756 + 3363*sqrt(2)) = 780.279406806795145659... and c = sqrt(112232 - 176706*sqrt(2) + sqrt(-24823369828 + 32297875299*sqrt(2)))/2744 = 0.02991158822483794318293134... . - Vaclav Kotesovec, Nov 28 2016

MAPLE

g():= seq(convert(n, base, 2)[1..4], n=17..31):

b:= proc(l) option remember;

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

    end:

a:= n-> b([n$4]):

seq(a(n), n=0..16);

MATHEMATICA

g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 4]], {n, 2^4 + 1, 2^5 - 1}];

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

a[n_] := b[Table[n, {4}]];

a /@ Range[0, 16] (* Jean-Fran├žois Alcover, Apr 25 2020, after Alois P. Heinz *)

CROSSREFS

Column k=4 of A263159.

Cf. A263064.

Sequence in context: A199098 A208784 A126681 * A232196 A222881 A229844

Adjacent sequences:  A263159 A263160 A263161 * A263163 A263164 A263165

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 11 2015

STATUS

approved

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Last modified May 21 09:30 EDT 2022. Contains 353908 sequences. (Running on oeis4.)