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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.
2
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
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
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Jan 28 2017
STATUS
approved