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 A327259 #52 Jul 10 2022 20:43:01
%S A327259 1,2,2,3,8,3,4,10,10,4,5,16,13,16,5,6,18,20,20,18,6,7,24,23,32,23,24,
%T A327259 7,8,26,30,36,36,30,26,8,9,32,33,48,41,48,33,32,9,10,34,40,52,54,54,
%U A327259 52,40,34,10,11,40,43,64,59,72,59,64,43,40,11,12,42,50,68,72,78,78,72,68,50,42,12
%N A327259 Array T(n,k) = 2*n*k - A319929(n,k), n >= 1, k >= 1, read by antidiagonals.
%C A327259 Associative multiplication-like table whose values depend on whether n and k are odd or even.
%C A327259 Associativity is proved by checking the formula with eight cases of three odd and even arguments. T(n,k) is distributive as long as partitioning an even number into two odd numbers is not allowed.
%C A327259 T(n,k) has the same group structure as A319929, A322630 and A322744. For those arrays, position (3,3) is 5, 7 and 11 respectively. T(3,3) = 13. If we didn't have the formula for these arrays, their entries could be computed knowing one position and applying the arithmetic rules.
%H A327259 David Lovler, <a href="/A327259/b327259.txt">Table of n, a(n) for n = 1..465</a> [restored by _Georg Fischer_, Oct 14 2019]
%F A327259 T(n,k) = 2*n*k - n - k + 1 if n is odd and k is odd;
%F A327259 T(n,k) = 2*n*k - n if n is even and k is odd;
%F A327259 T(n,k) = 2*n*k - k if n is odd and k is even;
%F A327259 T(n,k) = 2*n*k if n is even and k is even.
%F A327259 T(n,k) = 8*floor(n/2)*floor(k/2) + A319929(n,k).
%F A327259 T(n,n) = A354595(n). - _David Lovler_, Jul 09 2022
%F A327259 Writing T(n,k) as (4*n*k - 2*A319929(n,k))/2 shows that the array is U(4;n,k) of A327263. - _David Lovler_, Jan 15 2022
%e A327259 Array T(n,k) begins:
%e A327259 1 2 3 4 5 6 7 8 9 10
%e A327259 2 8 10 16 18 24 26 32 34 40
%e A327259 3 10 13 20 23 30 33 40 43 50
%e A327259 4 16 20 32 36 48 52 64 68 80
%e A327259 5 18 23 36 41 54 59 72 77 90
%e A327259 6 24 30 48 54 72 78 96 102 120
%e A327259 7 26 33 52 59 78 85 104 111 130
%e A327259 8 32 40 64 72 96 104 128 136 160
%e A327259 9 34 43 68 77 102 111 136 145 170
%e A327259 10 40 50 80 90 120 130 160 170 200
%t A327259 T[n_,k_]:=2n*k-If[Mod[n,2]==1,If[Mod[k,2]==1,n+k-1,k],If[Mod[k,2]==1,n,0]]; MatrixForm[Table[T[n,k],{n,1,10},{k,1,10}]] (* _Stefano Spezia_, Sep 05 2019 *)
%o A327259 (PARI) T(n,k) = 2*n*k - if (n%2, if (k%2, n+k-1, k), if (k%2, n, 0));
%o A327259 matrix(8, 8, n, k, T(n,k)) \\ _Michel Marcus_, Sep 04 2019
%Y A327259 Equals A322744 + A322630 - A319929.
%Y A327259 Equals 4*A322630 - 3*A319929.
%Y A327259 Cf. A327260, A327261, A327263.
%Y A327259 0 and diagonal is A354595.
%K A327259 nonn,tabl
%O A327259 1,2
%A A327259 _David Lovler_, Aug 27 2019