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A316673
Number of paths from (0,0,0) to (n,n,n) that always move closer to (n,n,n).
3
1, 13, 818, 64324, 5592968, 515092048, 49239783968, 4831678931008, 483371425775744, 49083260519243008, 5043379069021557248, 523221884090930480128, 54715789513061864081408, 5760456190025868833542144, 609948004367577499751948288, 64905519628343663567453569024
OFFSET
0,2
LINKS
FORMULA
Recurrence: see Maple program.
a(n) = A126086(n) * ceiling(2^(n-1)) = A126086(n) * A011782(n).
a(n) ~ sqrt((6 + 5*2^(1/3) + 4*2^(2/3))/6) * (24*2^(2/3) + 30*2^(1/3) + 38)^n / (4*Pi*n). - Vaclav Kotesovec, May 14 2020
MAPLE
a:= proc(n) option remember; `if`(n<4, [1, 13, 818, 64324][n+1],
(2*(3*n-2)*(57*n^2-95*n+25)*a(n-1)-4*(9*n^3-30*n^2+29*n-6)*
a(n-2)+8*(3*n-1)*(n-2)^2*a(n-3))/(n^2*(3*n-4)))
end:
seq(a(n), n=0..20);
MATHEMATICA
a[n_] := a[n] = If[n < 4, {1, 13, 818, 64324}[[n+1]], (2(3n-2)(57n^2- 95n+25) a[n-1] - 4(9n^3-30n^2+29n-6) a[n-2] + 8(3n-1)(n-2)^2 a[n-3]) / (n^2 (3n-4))];
a /@ Range[0, 20] (* Jean-François Alcover, May 14 2020, after Maple *)
CROSSREFS
Column k=3 of A316674.
Sequence in context: A221934 A328033 A366559 * A319509 A189446 A296803
KEYWORD
nonn,walk
AUTHOR
Alois P. Heinz, Jul 10 2018
STATUS
approved