The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A316673

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A316673

Number of paths from (0,0,0) to (n,n,n) that always move closer to (n,n,n).
(history; published version)

#15 by Michel Marcus at Thu May 14 05:35:43 EDT 2020

STATUS

reviewed

approved

#14 by Peter Luschny at Thu May 14 05:27:02 EDT 2020

STATUS

proposed

reviewed

#13 by Vaclav Kotesovec at Thu May 14 05:10:25 EDT 2020

STATUS

editing

proposed

#12 by Vaclav Kotesovec at Thu May 14 05:10:01 EDT 2020

FORMULA

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

STATUS

proposed

editing

#11 by Jean-François Alcover at Thu May 14 02:03:07 EDT 2020

STATUS

editing

proposed

#10 by Jean-François Alcover at Thu May 14 02:02:53 EDT 2020

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 *)

STATUS

approved

editing

#9 by Alois P. Heinz at Tue Jul 10 14:28:59 EDT 2018

STATUS

editing

approved

#8 by Alois P. Heinz at Tue Jul 10 10:51:23 EDT 2018

FORMULA

a(n) = A126086(n) * ceiling(2^(n-1)) = A126086(n) * A011782(n).

#7 by Alois P. Heinz at Tue Jul 10 10:50:22 EDT 2018

FORMULA

a(n) = A126086(n) * ceiling(2^(n-1)).

CROSSREFS

Cf. A052141, A126086.

#6 by Alois P. Heinz at Tue Jul 10 10:02:25 EDT 2018

CROSSREFS

Column k=3 of A316674.