A111158 - OEIS

%I #21 Mar 19 2022 13:46:59

%S 1,20,449,6792,67063,484419,2750715,12919671,52083292,185179593,

%T 592791088,1736022657,4710111660,11959634412,28654640036,65224656452,

%U 141850935657,296163412400,596041392921,1160330645548,2191579277799,4026627536451,7213267409435

%N Number of 5 X 5 magic squares with line sum n.

%D 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.

%H Alois P. Heinz, <a href="/A111158/b111158.txt">Table of n, a(n) for n = 0..10000</a>

%H M. Ahmed, J. De Loera, R. Hemmecke, <a href="https://arxiv.org/abs/math/0201108">Polyhedral Cones of Magic Cubes and Squares</a>, arXiv:0201108 [math.CO], 2002.

%H J. A. De Loera, D. Haws, R. Hemmecke, P. Huggins, B. Sturmfels et al., <a href="http://dx.doi.org/10.1016/j.jsc.2004.02.001">Short rational functions for toric algebra and applications</a>, J. Symb. Comput. 38 (2) (2004) 959-973

%F 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).

%Y Cf. A093199, A111086.

%K nonn

%O 0,2

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