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A229482 Number of lattice paths from {n}^3 to {0}^3 using steps that decrement one component or all components by the same positive integer. 2
1, 7, 248, 11380, 577124, 30970588, 1724240804, 98508192580, 5736813639188, 339068764626556, 20277072462706100, 1224258843324348388, 74504869395134442884, 4564559749008113090620, 281250580532881468554692, 17415330397418786646707236 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

Vaclav Kotesovec, Recurrence (of order 6)

FORMULA

a(n) ~ c*d^n/n, where d = (3*(375+sqrt(17))^(2/3)+156+23*(375+sqrt(17))^(1/3))/(375+sqrt(17))^(1/3) = 66.266905910039023... is the root of the equation -125 + 183*d - 69*d^2 + d^3 = 0 and c = 0.1272434612906147722352211214089... - Vaclav Kotesovec, Sep 25 2013

MAPLE

b:= proc(l) local m; m:= nops(l); if m=0 or l[m]=0 then 1

      elif m>1 then b(l):= add(add(b(sort(subsop(i=l[i]-j, l))),

      j=1..l[i]), i=1..m)+add(b(map(x->x-j, l)), j=1..l[1]) else 0 fi

    end:

a:= n-> b([n$3]):

seq(a(n), n=0..20);

CROSSREFS

Column k=3 of A229345.

Sequence in context: A203158 A227414 A203698 * A193371 A142805 A203474

Adjacent sequences:  A229479 A229480 A229481 * A229483 A229484 A229485

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 24 2013

STATUS

approved

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Last modified November 20 14:28 EST 2018. Contains 317402 sequences. (Running on oeis4.)