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
Keywords
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
- Index entries for linear recurrences with constant coefficients, signature (-8,-30,-66,-77,24,313,720,916,397,-1137,-3272,-4675,-3613,837,7577,13292,13848,6786,-6573,-20953,-29329,-26430,-11581,10660,32274,44919,43008,25727,-2415,-32633,-54500,-59685,-45482,-16327,17843,45794,59517,56629,39771,14215,-14215,-39771,-56629,-59517,-45794,-17843,16327,45482,59685,54500,32633,2415,-25727,-43008,-44919,-32274,-10660,11581,26430,29329,20953,6573,-6786,-13848,-13292,-7577,-837,3613,4675,3272,1137,-397,-916,-720,-313,-24,77,66,30,8,1).
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).