A126652 -id:A126652 - cp's OEIS frontend

A126653 A 3 X 3 magic square with magic sum 45: the Loh-Shu square A033812 multiplied by 3.

24, 3, 18, 9, 15, 21, 12, 27, 6

Offset: 1

Parthasarathy Nambi, Feb 08 2007

The magic sum is 45. See Figure C.6 in Appendix C in Maya Ahmed's PhD thesis.

			The magic square is:
24  3 18
9  15 21
12 27  6

Maya Mohsin Ahmed, Algebraic Combinatorics of Magic Squares, arXiv:math/0405476 [math.CO], 2004. PhD thesis.
Maya Mohsin Ahmed, How many squares are there, Mr. Franklin?: Constructing and Enumerating Franklin Squares, Amer. Math. Monthly, Vol. 111, 2004, pp. 394-410.
Index entries for sequences related to magic squares

Cf. A126652 for 5*A033812.

a(n) = 3*A033812(n). - M. F. Hasler, Jan 26 2019

Edited by M. F. Hasler, Jan 26 2019

A126709 The Loh-Shu 3 x 3 magic square, variant 2.

Original entry on oeis.org

4, 9, 2, 3, 5, 7, 8, 1, 6

Offset: 1

Parthasarathy Nambi, Feb 12 2007

The magic sum is 15. See Figure 1.2 on page 10 in Maya Ahmed's PhD thesis. This magic square is referred to Loh-Shu magic square and is attributed to the legendary Fu Xi (Fuh-Hi).

Sequence A033812 lists the same magic square with rows in reversed order, i.e., vertically flipped. - M. F. Hasler, Jan 26 2019

			The magic square is:
  4 9 2
  3 5 7
  8 1 6

Maya Mohsin Ahmed, Algebraic Combinatorics of Magic Squares, arXiv:math/0405476 [math.CO], 2004.
Alexander Poddiakov, Self-Similar Structures of Nontransitive Dice Sets: Examples of Nested "Rock-Paper-Scissors" Relations Based on Numbers from The Lo Shu Magic Square,
Index entries for sequences related to magic squares

A033812 is the same magic square with rows listed in reverse order.
Other magic 3 X 3 squares: A126648, A126652, A126653, A126654.
Larger magic squares: A126647, A126649, A126651, A126650.

Edited by M. F. Hasler, Jan 26 2019

A033812 The Loh-Shu 3 X 3 magic square, lexicographically largest variant when read by columns.

Original entry on oeis.org

8, 1, 6, 3, 5, 7, 4, 9, 2

Offset: 1

Olivier Gorin (gorin(AT)roazhon.inra.fr)

Of course there are a large number of ways to convert this (unique) magic square to a sequence by reading it by rows, so the sequence is hardly unique. - N. J. A. Sloane, Aug 29 2002
This magic square is referred to Loh-Shu magic square and is attributed to the legendary Fu Xi (Fuh-Hi).
Among all the equivalent variants of this magic square (modulo rotations and reflections) this one can be characterized as the lexicographically largest one when read by columns, i.e., (8, 3, 4, 1, ...), while the lexicographically smallest one would be (2, 7, 6, 9, ...). - M. F. Hasler, Jan 26 2019

			The magic square is
[ 8 1 6 ]
[ 3 5 7 ]
[ 4 9 2 ]

Harvey Heinz, Prime Magic Squares
Index entries for sequences related to magic squares

Cf. A126709.

Sequences A126652 and adjacent list several multiples and other affine transforms of this one.

Edited by M. F. Hasler, Jan 26 2019

A126710 A 4 x 4 magic square.

Original entry on oeis.org

7, 12, 1, 14, 2, 13, 8, 11, 16, 3, 10, 5, 9, 6, 15, 4

Offset: 1

Parthasarathy Nambi, Feb 12 2007

The magic sum is 34. See Figure 1.2 on page 10 in Maya Ahmed's PhD thesis. This magic square is found in a Jaina inscription of the twelfth or thirteenth century in the city of Khajuraho, India (as mentioned in Maya Ahmed's thesis).

The inscription is in the Parsvanatha Temple and may date back to its construction, estimated at 954. - Charles R Greathouse IV, Dec 24 2018

			The magic square is:
7 12 1 14
2 13 8 11
16 3 10 5
9 6 15 4

Maya Mohsin Ahmed, Algebraic combinatorics of magic squares, PhD thesis UC Davis, arXiv:math/0405476 [math.CO], 2004.
W. S. Andrews, Magic Squares And Cubes, 1917, pp. 124-126.
Rainer Typke, Magic Square at the Parsvanatha Temple, Khajuraho, Eastern Group, 2008.

Cf. A126654, A126653, A126652, A126651, A126650, A126649, A126648, A126647.

A126976 A 6 x 6 magic square read by rows.

Original entry on oeis.org

6, 32, 3, 34, 35, 1, 7, 11, 27, 28, 8, 30, 19, 14, 16, 15, 23, 24, 18, 20, 22, 21, 17, 13, 25, 29, 10, 9, 26, 12, 36, 5, 33, 4, 2, 31

Offset: 1

Parthasarathy Nambi, Mar 20 2007

The magic sum is 111.

			The magic square is:
6 32 3 34 35 1
7 11 27 28 8 30
19 14 16 15 23 24
18 20 22 21 17 13
25 29 10 9 26 12
36 5 33 4 2 31

Wikipedia, Magic Square.

Cf. A126651, A126652, A126653, A126654, A126709, A126710, A125519, A125522, A126275, A126276.

A126977 A 3 x 3 multiplicative magic square read by rows.

Original entry on oeis.org

2, 9, 12, 36, 6, 1, 3, 4, 18

Offset: 1

Parthasarathy Nambi, Mar 20 2007

The magic product is 216.

			The magic square is:
2 9 12
36 6 1
3 4 18

Wikipedia, Magic squares.

Cf. A126651, A126652, A126653, A126654, A126709, A126710, A125519, A125522, A126275, A126276.

A116198 A 3 x 3 magic square read by rows.

Original entry on oeis.org

7, 0, 5, 2, 4, 6, 3, 8, 1

Offset: 1

Parthasarathy Nambi, Apr 08 2007

The magic sum is 12.

			The magic square is:
7 0 5
2 4 6
3 8 1

Guoce Xin, Constructing All Magic Squares of Order Three.

Cf. A126710, A126976, A126977, A126647, A126648, A126649, A126650, A126651, A126652, A126653, A126654, A126709.

A127907 A 5 x 5 magic square read by rows.

Original entry on oeis.org

17, 24, 1, 8, 15, 23, 5, 7, 14, 16, 4, 6, 13, 20, 22, 10, 12, 19, 21, 3, 11, 18, 25, 2, 9

Offset: 1

Parthasarathy Nambi, Apr 05 2007

The magic sum is 65.

			The magic square is:
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9

Wacław Sierpiński, Czym sie zajmuje teoria liczb. Warsaw: PW "Wiedza Powszechna", 1957, p. 17.

Colm Mulcahy, Quasi-Masked Forcing Kind of Magic Squares.

Cf. A126647, A126648, A126649, A126650, A126651, A126652, A126653, A126654, A126709, A126710, A126976, A126977.

A128883 A 4 X 4 magic square with sum 33 read by rows.

Original entry on oeis.org

1, 14, 14, 4, 11, 7, 6, 9, 8, 10, 10, 5, 13, 2, 3, 15

Offset: 1

Parthasarathy Nambi, Apr 18 2007

			The magic square is:
1 14 14 4
11 7 6 9
8 10 10 5
13 2 3 15

A. Skalli, Magic cube with Gaudi's square
Wikipedia, The Sagrada Familia magic square.

Cf. A126710, A126976, A126977, A126647, A126648, A126649, A126650, A126651, A126652, A126653, A126654, A126709.

cp's OEIS Frontend

A126653 A 3 X 3 magic square with magic sum 45: the Loh-Shu square A033812 multiplied by 3.

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A126709 The Loh-Shu 3 x 3 magic square, variant 2.

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A033812 The Loh-Shu 3 X 3 magic square, lexicographically largest variant when read by columns.

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A126710 A 4 x 4 magic square.

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A126976 A 6 x 6 magic square read by rows.

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A126977 A 3 x 3 multiplicative magic square read by rows.

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A116198 A 3 x 3 magic square read by rows.

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A127907 A 5 x 5 magic square read by rows.

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A128883 A 4 X 4 magic square with sum 33 read by rows.

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