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A160540 The number of distinct n X n panmagic = pandiagonal = diabolic = Nasik squares, not counting rotations, reflections, or row/column cyclings of others, with the additional property that each i X j rectangle, including each "wrap-around" i X j rectangle, where i and j are positive integers whose product is n, also sums to the magic constant A006003(n) = n(n^2+1)/2. 0
1, 0, 0, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A "row/column cycling" of another square is a square that can be formed by moving any number of rows from the top of the other square to the bottom of it and keeping them in the same order, or by moving any number of columns from the left of it to the right of it and keeping them in the same order, or by doing both. Since these squares are panmagic, and so the "wrap-around" diagonals also must sum to the magic constant, row/column cyclings of a square are not essentially different from that square.

LINKS

Table of n, a(n) for n=1..4.

EXAMPLE

a(4) = 3 because there are 3 distinct 4 X 4 panmagic squares, not counting rotations, reflections, or row/column cyclings of others, with the additional property that each 2 X 2 square, including each "wrap around" 2 X 2 square such as the one consisting of a11, a12, a41, and a42, and the one consisting of a11, a14, a41, and a44, also sums to A006003(4) = 4(4^2+1)/2 = 34:

     1  8 10 15       1  8 11 14       1  8 13 12

    12 13  3  6      12 13  2  7      14 11  2  7

     7  2 16  9       6  3 16  9       4  5 16  9

    14 11  5  4      15 10  5  4      15 10  3  6

The following panmagic square does not count because it can be formed from the third panmagic square given above by moving the first column on the left of it to the right of it and then reflecting it in the y-axis:

     1 12 13  8

    14  7  2 11

     4  9 16  5

    15  6  3 10

CROSSREFS

Cf. A027567.

Sequence in context: A100267 A176935 A257228 * A186718 A319625 A307802

Adjacent sequences:  A160537 A160538 A160539 * A160541 A160542 A160543

KEYWORD

more,nonn,bref

AUTHOR

Anonymous, May 18 2009

STATUS

approved

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Last modified November 13 20:57 EST 2019. Contains 329106 sequences. (Running on oeis4.)