A281725 Triangular array T(n,k) is the sum of elements in an n X k matrix that will be assigned the same value whether the integers from 1 to n*k are assigned to elements in row-major order or column-major order.

1, 3, 5, 6, 7, 15, 10, 9, 13, 34, 15, 11, 24, 21, 65, 21, 13, 19, 25, 31, 111, 28, 15, 33, 58, 54, 43, 175, 36, 17, 25, 33, 41, 49, 57, 260, 45, 19, 42, 37, 115, 55, 96, 73, 369, 55, 21, 31, 82, 51, 61, 142, 81, 91, 505, 66, 23, 51, 45, 84, 201, 117, 89, 150, 111, 671

Offset: 1

Author

Michel Marcus, Jan 28 2017

Keywords

• nonn
• tabl

Examples

			For n=2 and k=3, the matrix will be
1 2 3  and  1 3 5
4 5 6       2 4 6
and there are 2 identical terms, 1 and 6, whose sum is 7.
The triangle begins
   1;
   3,  5;
   6,  7, 15;
  10,  9, 13, 34;
  15, 11, 24, 21, 65;
  21, 13, 19, 25, 31, 111;
  ...
		

Links

• Alois P. Heinz, Antidiagonals n = 1..141, flattened
• Ana Rechtman, 3ème Défi du Calendrier Mathématique, Images des Mathématiques, CNRS, January 2017.

Crossrefs

Cf. A281726.

Main diagonal gives A006003.

Column k=1 gives A000217.

T(2n,n) gives A058331 for n>0.

T(2n+1,n+1) gives A081436.

Programs

Maple

T:= (n, k)-> add(add(`if`(j+k*(i-1)=
    i+n*(j-1), j+k*(i-1), 0), i=1..n), j=1..k):
seq(seq(T(n,k), k=1..n), n=1..20);  # Alois P. Heinz, Jan 28 2017

PARI

a(n, k) = {ml = matrix(n, k, i, j, ((i-1)*k+j)); mc = matrix(n, k, i, j, ((j-1)*n+i)); sum(i=1, n, sum(j=1, k, ml[i,j]*(ml[i,j] == mc[i,j])));}