OFFSET
1,2
COMMENTS
T(n,k) is commutative, associative, has identity element 1 and has 0. Also it is distributive except when an even number is partitioned into two odd numbers. Thus it has a multiplicative structure similar to that of A319929, A322630, A322744 and A327259 except that T(odd,odd) is not always odd, T(even,even) is not always even and T(odd,even) is not always even.
LINKS
David Lovler, Table of n, a(n) for n = 1..465
FORMULA
EXAMPLE
Array begins:
1 2 3 4 5 6 7 8 9 10 ...
2 3 5 6 8 9 11 12 14 15 ...
3 5 8 10 13 15 18 20 23 25 ...
4 6 10 12 16 18 22 24 28 30 ...
5 8 13 16 21 24 29 32 37 40 ...
6 9 15 18 24 27 33 36 42 45 ...
7 11 18 22 29 33 40 44 51 55 ...
8 12 20 24 32 36 44 48 56 60 ...
9 14 23 28 37 42 51 56 65 70 ...
10 15 25 30 40 45 55 60 70 75 ...
...
MATHEMATICA
Table[Function[n, ((3/2)*n*k + (1/2)*If[OddQ@ n, If[OddQ@ k, n + k - 1, k], If[OddQ@ k, n, 0]])/2][m - k + 1], {m, 11}, {k, m}] // Flatten (* Michael De Vlieger, Jun 23 2020 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
David Lovler, May 16 2020
STATUS
approved