|
%I #6 May 26 2021 02:28:55
%S 0,1,1,2,3,2,4,5,5,4,6,7,8,7,6,9,10,11,11,10,9,12,13,14,15,14,13,12,
%T 16,17,18,19,19,18,17,16,20,21,22,23,24,23,22,21,20,25,26,27,28,29,29,
%U 28,27,26,25,30,31,32,33,34,35,34,33,32,31,30,36,37,38,39,40,41,41,40,39,38,37,36
%N Array read by antidiagonals T(n,k) = ((n+k+1)^2 - (n+k+1) mod 2)/4 + min(n,k) for n and k >= 0.
%H Jianrui Xie, <a href="https://arxiv.org/abs/2105.10752">On Symmetric Invertible Binary Pairing Functions</a>, arXiv:2105.10752 [math.CO], 2021.
%e Array begins:
%e 0 1 2 4 6 ...
%e 1 3 5 7 10 ...
%e 2 5 8 11 14 ...
%e 4 7 11 15 19 ...
%e 6 10 14 19 24 ...
%e ...
%t T[n_, k_] := ((n + k + 1)^2 - Mod[n + k + 1, 2])/4 + Min[n, k]; Table[T[k, n - k], {n, 0, 11}, {k, 0, n}] // Flatten (* _Amiram Eldar_, May 25 2021 *)
%o (PARI) T(n,k) = ((n+k+1)^2 - (n+k+1)%2)/4 + min(n,k);
%Y Cf. A128282 (another pairing function).
%K nonn,tabl
%O 0,4
%A _Michel Marcus_, May 25 2021
|
