A344646 - OEIS

%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