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

1,2

Links

Alois P. Heinz, Antidiagonals n = 1..141, flattened

Ana Rechtman, 3ème Défi du Calendrier Mathématique, Images des Mathématiques, CNRS, January 2017.

Example

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;
  ...

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

Prog

(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]))); }

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.

Sequence in context: A086188 A154535 A006754 * A274928 A163620 A227722

Adjacent sequences: A281722 A281723 A281724 * A281726 A281727 A281728

Keyword

nonn,tabl

Author

Michel Marcus, Jan 28 2017

Status

approved