The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A348712

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A348712

Square array read by falling antidiagonals: T(n,k) is the number of bounded regions formed by the Lissajous curve x=cos(n*t), y=sin(k*t).
(history; published version)

#16 by Joerg Arndt at Sat Oct 28 05:13:36 EDT 2023

STATUS

reviewed

approved

#15 by Michel Marcus at Sat Oct 28 04:12:44 EDT 2023

STATUS

proposed

reviewed

#14 by Jean-François Alcover at Sat Oct 28 01:55:38 EDT 2023

STATUS

editing

proposed

#13 by Jean-François Alcover at Sat Oct 28 01:55:29 EDT 2023

MATHEMATICA

T[n_, k_] := T[n, k] = With[{m = GCD[n, k]}, Which[OddQ[n] && m == 1, (n-1)*(k-1)+n*k, EvenQ[n] && m == 1, (n-1)*(k-1)/2, True, T[n/m, k/m]]];

Table[Table[T[k, n - k + 1], {k, 1, n}], {n, 1, 12}] // Flatten (* Jean-François Alcover, Oct 28 2023 *)

STATUS

approved

editing

#12 by N. J. A. Sloane at Mon Nov 01 00:38:00 EDT 2021

STATUS

reviewed

approved

#11 by Andrey Zabolotskiy at Sun Oct 31 19:21:13 EDT 2021

STATUS

proposed

reviewed

#10 by Rémy Sigrist at Sun Oct 31 14:03:04 EDT 2021

STATUS

editing

proposed

#9 by Rémy Sigrist at Sun Oct 31 14:02:53 EDT 2021

CROSSREFS

Cf. A007678, A300153.

STATUS

approved

editing

Discussion

Sun Oct 31

14:03

Rémy Sigrist: added xref

#8 by Peter Luschny at Sun Oct 31 13:41:54 EDT 2021

STATUS

editing

approved

#7 by Peter Luschny at Sun Oct 31 13:41:48 EDT 2021

MAPLE

T := proc(n, k) option remember; igcd(n, k); if % = 1 then (n-1)*(k-1);

ifelse(n::even, % / 2, % + n*k) else T(n / %, k / %) fi end:

seq(seq(T(k, n - k + 1), k = 1..n), n = 1..12); # Peter Luschny, Oct 31 2021

STATUS

reviewed

editing