This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A348712 #16 Oct 28 2023 05:13:36
%S A348712 1,2,0,3,1,3,4,1,8,0,5,2,1,0,5,6,2,18,3,14,0,7,3,23,1,23,3,7,8,3,2,6,
%T A348712 32,0,20,0,9,4,33,1,1,8,33,0,9,10,4,38,9,50,10,46,7,26,0,11,5,3,2,59,
%U A348712 1,59,0,3,5,11,12,5,48,12,68,15,72,14,60,9,32,0
%N 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).
%H A348712 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lissajous_curve">Lissajous curve</a>
%F A348712 T(n,k) = (n-1)*(k-1) + n*k when n is odd and GCD(n,k) = 1.
%F A348712 T(n,k) = (n-1)*(k-1)/2 when n is even and GCD(n,k) = 1.
%F A348712 T(n,k) = T(n/m,k/m) when GCD(n,k) = m.
%e A348712 Array begins:
%e A348712 +-----+---------------------------------------------------------------+
%e A348712 | n\k | 1 2 3 4 5 6 7 8 9 10 11 12 .. |
%e A348712 +-----+---------------------------------------------------------------+
%e A348712 | 1 | 1 2 3 4 5 6 7 8 9 10 11 12 .. |
%e A348712 | 2 | 0 1 1 2 2 3 3 4 4 5 5 6 .. |
%e A348712 | 3 | 3 8 1 18 23 2 33 38 3 48 53 4 .. |
%e A348712 | 4 | 0 0 3 1 6 1 9 2 12 2 15 3 .. |
%e A348712 | 5 | 5 14 23 32 1 50 59 68 77 2 95 104 .. |
%e A348712 | 6 | 0 3 0 8 10 1 15 18 1 23 25 2 .. |
%e A348712 | 7 | 7 20 33 46 59 72 1 98 111 124 137 150 .. |
%e A348712 | 8 | 0 0 7 0 14 3 21 1 28 6 35 1 .. |
%e A348712 | 9 | 9 26 3 60 77 8 111 128 1 162 179 18 .. |
%e A348712 | 10 | 0 5 9 14 0 23 27 32 36 1 45 50 .. |
%e A348712 | 11 | 11 32 53 74 95 116 137 158 179 200 1 242 .. |
%e A348712 | 12 | 0 0 0 3 22 0 33 8 3 10 55 1 .. |
%e A348712 | .. | .. .. .. .. .. .. .. .. .. .. .. .. .. |
%e A348712 +---------------------------------------------------------------------+
%p A348712 T := proc(n, k) option remember; igcd(n, k); if % = 1 then (n-1)*(k-1);
%p A348712 ifelse(n::even, % / 2, % + n*k) else T(n / %, k / %) fi end:
%p A348712 seq(seq(T(k, n - k + 1), k = 1..n), n = 1..12); # _Peter Luschny_, Oct 31 2021
%t A348712 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]]];
%t A348712 Table[Table[T[k, n - k + 1], {k, 1, n}], {n, 1, 12}] // Flatten (* _Jean-François Alcover_, Oct 28 2023 *)
%Y A348712 Cf. A007678, A300153.
%K A348712 nonn,tabl,easy
%O A348712 1,2
%A A348712 _Mohammed Yaseen_, Oct 31 2021