A111158 Number of 5 X 5 magic squares with line sum n.

1, 20, 449, 6792, 67063, 484419, 2750715, 12919671, 52083292, 185179593, 592791088, 1736022657, 4710111660, 11959634412, 28654640036, 65224656452, 141850935657, 296163412400, 596041392921, 1160330645548, 2191579277799, 4026627536451, 7213267409435

Offset

0,2

References

Maya Ahmed, Jesús De Loera and Raymond Hemmecke, Polyhedral cones of magic cubes and squares, in Discrete and Computational Geometry, Springer, Berlin, 2003, pp. 25-41.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

M. Ahmed, J. De Loera, R. Hemmecke, Polyhedral Cones of Magic Cubes and Squares, arXiv:0201108 [math.CO], 2002.

J. A. De Loera, D. Haws, R. Hemmecke, P. Huggins, B. Sturmfels et al., Short rational functions for toric algebra and applications, J. Symb. Comput. 38 (2) (2004) 959-973

Formula

G.f.: -(1 + 28*t + 639*t^2 + 11050*t^3 + 136266*t^4 + 1255833*t^5 + 9120009*t^6 + 54389347*t^7 + 274778754*t^8 + 1204206107*t^9 + 4663304831*t^10 + 16193751710*t^11 + 51030919095*t^12 + 147368813970*t^13 + 393197605792*t^14 + 975980866856*t^15 + 2266977091533*t^16 + 4952467350549*t^17 + 10220353765317*t^18 + 20000425620982*t^19 + 37238997469701*t^20 + 66164771134709*t^21 + 112476891429452*t^22 + 183365550921732*t^23 + 287269293973236*t^24 + 433289919534912*t^25 + 630230390692834*t^26 + 885291593024017*t^27 + 1202550133880678*t^28 + 1581424159799051*t^29 + 2015395674628040*t^30 + 2491275358809867*t^31 + 2989255690350053*t^32 + 3483898479782320*t^33 + 3946056312532923*t^34 + 4345559454316341*t^35 + 4654344257066635*t^36 + 4849590327731195*t^37 + 4916398325176454*t^38 + 4849590327731195*t^39 + 4654344257066635*t^40 + 4345559454316341*t^41 + 3946056312532923*t^42 + 3483898479782320*t^43 + 2989255690350053*t^44 + 2491275358809867*t^45 + 2015395674628040*t^46 + 1581424159799051*t^47 + 1202550133880678*t^48 + 885291593024017*t^49 + 630230390692834*t^50 + 433289919534912*t^51 + 287269293973236*t^52 + 183365550921732*t^53 + 112476891429452*t^54 + 66164771134709*t^55 + 37238997469701*t^56 + 20000425620982*t^57 + 10220353765317*t^58 + 4952467350549*t^59 + 2266977091533*t^60 + 975980866856*t^61 + 393197605792*t^62 + 147368813970*t^63 + 51030919095*t^64 + 16193751710*t^65 + 4663304831*t^66 + 1204206107*t^67 + 274778754*t^68 + 54389347*t^69 + 9120009*t^70 + 1255833*t^71 + 136266*t^72 + 11050*t^73 + 639*t^74 + 28*t^75 + t^76) / ((-1 + t^2)^6*(t^2 + t + 1)^7*(t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)^2*(t^6 + t^3 + 1)*(t^4 + t^3 + t^2 + t + 1)^4*(-1 + t)^9*(t + 1)^4*(t^2 + 1)^4).

Crossrefs

Cf. A093199, A111086.

Sequence in context: A320765 A099278 A276452 * A049382 A288034 A272553

Adjacent sequences: A111155 A111156 A111157 * A111159 A111160 A111161

Keyword

nonn

Author

N. J. A. Sloane, using g.f. supplied by Jesús De Loera (deloera(AT)math.ucdavis.edu), Oct 22 2005

Status

approved