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A108578 Number of 3 X 3 magic squares with magic sum 3n. 7
0, 0, 0, 0, 8, 24, 32, 56, 80, 104, 136, 176, 208, 256, 304, 352, 408, 472, 528, 600, 672, 744, 824, 912, 992, 1088, 1184, 1280, 1384, 1496, 1600, 1720, 1840, 1960, 2088, 2224, 2352, 2496, 2640, 2784, 2936, 3096, 3248, 3416, 3584, 3752, 3928, 4112, 4288 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Contribution from Thomas Zaslavsky, Mar 12 2010: (Start)

A magic square has distinct positive integers in its cells, whose sum is the same (the "magic sum") along any row, column, or main diagonal.

a(n) is given by a quasipolynomial of period 6. (End)

LINKS

T. Zaslavsky, Table of n, a(n) for n = 1..10000.

M. Beck and T. Zaslavsky, An enumerative geometry for magic and magilatin labellings, Ann. Combinatorics, 10 (2006), no. 4, 395-413. MR 2007m:05010. Zbl 1116.05071. - Thomas Zaslavsky, Jan 29 2010

M. Beck and T. Zaslavsky, Six little squares and how their numbers grow, submitted. - Thomas Zaslavsky, Jan 29 2010

Matthias Beck and Thomas Zaslavsky, Six Little Squares and How their Numbers Grow, Journal of Integer Sequences, 13 (2010), Article 10.6.2.

FORMULA

G.f.: [8*x^5*(1+2*x)] / [(1-x)*(1-x^2)*(1-x^3)].

EXAMPLE

a(5) = 8 because there are 8 3 X 3 magic squares with entries 1,...,9 and magic sum 15.

PROG

(PARI) a(n)=(1/9)*(2*n^2-32*n+[144, 78, 120, 126, 96, 102][(n%18)/3+1])

CROSSREFS

Equals 8 times the second differences of A055328.

Cf. A108576, A108577, A108579.

Sequence in context: A128690 A283078 A140403 * A044450 A134223 A050427

Adjacent sequences:  A108575 A108576 A108577 * A108579 A108580 A108581

KEYWORD

nonn

AUTHOR

Thomas Zaslavsky and Ralf Stephan, Jun 11 2005

EXTENSIONS

Edited by N. J. A. Sloane, Feb 05 2010

Corrected g.f. to account for previous change in parameter n from magic sum s to s/3; by Thomas Zaslavsky, Mar 12 2010

STATUS

approved

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Last modified March 24 03:50 EDT 2017. Contains 283984 sequences.