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A321723 Number of non-normal magic squares whose entries are all 0 or 1 and sum to n. 6
1, 1, 0, 0, 9, 20, 96, 656, 5584, 48913, 494264, 5383552, 65103875, 840566080, 11834159652, 176621049784, 2838040416201, 48060623405312 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A non-normal magic square is a square matrix with row sums, column sums, and both diagonals all equal to d, for some d|n.

LINKS

Table of n, a(n) for n=0..17.

Wikipedia, Magic square

Index entries for sequences related to magic squares

FORMULA

a(n) >= A007016(n) with equality if n is prime. - Chai Wah Wu, Jan 15 2019

EXAMPLE

The a(4) = 9 magic squares:

  [1 1]

  [1 1]

.

  [1 0 0 0][1 0 0 0][0 1 0 0][0 1 0 0][0 0 1 0][0 0 1 0][0 0 0 1][0 0 0 1]

  [0 0 1 0][0 0 0 1][0 0 1 0][0 0 0 1][1 0 0 0][0 1 0 0][1 0 0 0][0 1 0 0]

  [0 0 0 1][0 1 0 0][1 0 0 0][0 0 1 0][0 1 0 0][0 0 0 1][0 0 1 0][1 0 0 0]

  [0 1 0 0][0 0 1 0][0 0 0 1][1 0 0 0][0 0 0 1][1 0 0 0][0 1 0 0][0 0 1 0]

MATHEMATICA

prs2mat[prs_]:=Table[Count[prs, {i, j}], {i, Union[First/@prs]}, {j, Union[Last/@prs]}];

multsubs[set_, k_]:=If[k==0, {{}}, Join@@Table[Prepend[#, set[[i]]]&/@multsubs[Drop[set, i-1], k-1], {i, Length[set]}]];

Table[Length[Select[Subsets[Tuples[Range[n], 2], {n}], And[Union[First/@#]==Range[Max@@First/@#]==Union[Last/@#], SameQ@@Join[{Tr[prs2mat[#]], Tr[Reverse[prs2mat[#]]]}, Total/@prs2mat[#], Total/@Transpose[prs2mat[#]]]]&]], {n, 5}]

CROSSREFS

Cf. A006052, A007016, A057151, A068313, A101370, A104602, A120732, A271103, A319056, A319616.

Cf. A321717, A321718, A321719, A321720, A321721, A321722.

Sequence in context: A013573 A146388 A230833 * A282763 A013338 A008847

Adjacent sequences:  A321720 A321721 A321722 * A321724 A321725 A321726

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 18 2018

EXTENSIONS

a(7)-a(15) from Chai Wah Wu, Jan 15 2019

a(16)-a(17) from Chai Wah Wu, Jan 16 2019

STATUS

approved

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Last modified June 19 03:38 EDT 2021. Contains 345125 sequences. (Running on oeis4.)