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
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
Programs
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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])));}