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 A351786 #11 Feb 23 2022 10:51:28
%S A351786 0,0,0,0,1,0,0,2,2,0,0,3,8,3,0,0,4,10,10,4,0,0,5,1,12,1,5,0,0,6,3,5,5,
%T A351786 3,6,0,0,7,9,18,16,18,9,7,0,0,8,11,15,20,20,15,11,8,0,0,9,32,25,17,65,
%U A351786 17,25,32,9,0,0,10,34,40,21,23,23,21,40,34,10,0
%N A351786 Symmetric array T(n, k), n, k >= 0, read by antidiagonals; for any m >= 0 with binary expansion Sum_{i >= 0} b_i*2^i, let d(m) = Sum_{i >= 0} b_i * 2^A130472(i); let t be the inverse of d; T(n, k) = t(d(n) * d(k)).
%C A351786 The function d is a bijection from the nonnegative integers to the nonnegative dyadic rationals satisfying d(A000695(n)) = n for any n >= 0.
%H A351786 Rémy Sigrist, <a href="/A351786/b351786.txt">Table of n, a(n) for n = 0..10010</a>
%H A351786 Rémy Sigrist, <a href="/A351786/a351786.png">Colored representation of the table for n, k < 2^10</a> (where the hue is function of T(n, k))
%H A351786 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dyadic_rational">Dyadic rational</a>
%H A351786 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A351786 T(A000695(n), A000695(k)) = A000695(n * k).
%F A351786 T(n, k) = T(k, n).
%F A351786 T(m, T(n, k)) = T(T(m, n), k).
%F A351786 T(n, 0) = 0.
%F A351786 T(n, 1) = n.
%e A351786 Array T(n, k) begins:
%e A351786 n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
%e A351786 ---+-------------------------------------------------------------------------
%e A351786 0| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e A351786 1| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
%e A351786 2| 0 2 8 10 1 3 9 11 32 34 40 42 33 35 41 43
%e A351786 3| 0 3 10 12 5 18 15 25 40 43 33 38 45 58 48 51
%e A351786 4| 0 4 1 5 16 20 17 21 2 6 3 7 18 22 19 23
%e A351786 5| 0 5 3 18 20 65 23 70 10 15 12 25 30 75 72 77
%e A351786 6| 0 6 9 15 17 23 28 74 34 37 43 56 51 96 62 105
%e A351786 7| 0 7 11 25 21 70 74 88 42 56 38 52 63 109 99 113
%e A351786 8| 0 8 32 40 2 10 34 42 128 136 160 168 130 138 162 170
%e A351786 9| 0 9 34 43 6 15 37 56 136 131 170 164 142 144 173 178
%e A351786 10| 0 10 40 33 3 12 43 38 160 170 130 137 163 172 132 142
%o A351786 (PARI) d(n) = { my (v=0, k); while (n, n-=2^k=valuation(n, 2); v+=2^((-1)^k*(k+1)\2)); v }
%o A351786 t(n) = { my (v=0, k); while (n, n-=2^k=valuation(n, 2); v+=2^if (k>=0, 2*k, -1-2*k)); v }
%o A351786 T(n,k) = t(d(n)*d(k))
%Y A351786 Cf. A000695, A130472, A351705, A351706, A351785 (addition).
%K A351786 nonn,base,tabl
%O A351786 0,8
%A A351786 _Rémy Sigrist_, Feb 19 2022