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A216039 Number of 6 by 6 magic squares with line sum n. 0
1, 96, 14763, 957936, 33177456, 718506720, 10837963166, 122793273216, 1103391397593, 8187061491760, 51724720525317, 284976371277888, 1395347280436638, 6165194801711616, 24889894891691712, 92768491235726640, 321987367305139071, 1048378447871747424, 3222195250935497833, 9398840830661453088 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..19.

G. Xin, A Euclid style algorithm for MacMahon partition analysis, arxiv 1208.6074

FORMULA

G.f.: (x^138+99*x^137+15057*x^136+1002806*x^135+36140317*x^134+823860011*x^133+13197261179*x^132+159778881431*x^131+1540197926928*x^130+12283604989433*x^129+83443844586997*x^128

+493826644119635*x127+2591895971809073*x^126+12239625173465375*x^125+52618101897021930*x^124

+207948182505922572*x^123+761697282842373791*x^122+2603936594202983265*x^121

+8357520624415623570*x^120+25313244131813040492*x^119+72673216612249799707*x^118

+198540029295827265030*x^117+517913155627899876744*x^116+1293950334879519037064*x^115

+3104565556800370034675*x^114+7170548645642540233444*x^113+15977552472766155842750*x^112

+34412717940513453504180*x^111+71769782821380635837621*x^110+145167679454737704278880*x^109

+285189004474854548554157*x^108+544883332503752228347324*x^107

+1013692519414068545966383*x^106+1838319814003865364502115*x^105

+3253035784774708879439262*x^104+5622314253334154424175766*x^103

+9498907763273239021574685*x^102+15700357961071728256043309*x^101

+25406320589195514110356366*x^100+40277791473075750762252075*x^99

+62597197699253178187339298*x^98+95425280193517651890574674*x^97

+142766762407648666487568356*x^96+209732150155458679271033099*x^95

+302678001784712603830421513*x^94+429303207319389562327707454*x^93

+598674963030494000816618195*x^92+821156092631443052249172731*x^91

+1108206045308608891199410839*x^90+1472032087920610932242371227*x^89

+1925075439230166802560415829*x^88+2479329488091630543216144069*x^87

+3145503368703854928491254853*x^86+3932062984462037001968113054*x^85

+4844201407852058337442332388*x^84+5882809249486653844574028923*x^83

+7043530583232146694988816214*x^82+8315998814445857390844541404*x^81

+9683347293907738803126233896*x^80+11122080015097990434647761713*x^79

+12602367905141556425711508726*x^78+14088806780184052230859053795*x^77

+15541636034748392591830628113*x^76+16918375811338196658691711642*x^75

+18175798884655835561351408187*x^74+19272116367842845200134757907*x^73

+20169228060755970451363952559*x^72+20834872558688610557869003806*x^71

+21244511627696474156825956913*x^70+21382798694422310755770332936*x^69

+21244511627696474156825956913*x^68+20834872558688610557869003806*x^67

+20169228060755970451363952559*x^66+19272116367842845200134757907*x^65

+18175798884655835561351408187*x^64+16918375811338196658691711642*x^63

+15541636034748392591830628113*x^62+14088806780184052230859053795*x^61

+12602367905141556425711508726*x^60+11122080015097990434647761713*x^59

+9683347293907738803126233896*x^58+8315998814445857390844541404*x^57

+7043530583232146694988816214*x^56+5882809249486653844574028923*x^55

+4844201407852058337442332388*x^54+3932062984462037001968113054*x^53

+3145503368703854928491254853*x^52+2479329488091630543216144069*x^51

+1925075439230166802560415829*x^50+1472032087920610932242371227*x^49

+1108206045308608891199410839*x^48+821156092631443052249172731*x^47

+598674963030494000816618195*x^46+429303207319389562327707454*x^45

+302678001784712603830421513*x^44+209732150155458679271033099*x^43

+142766762407648666487568356*x^42+95425280193517651890574674*x^41

+62597197699253178187339298*x^40+40277791473075750762252075*x^39

+25406320589195514110356366*x^38+15700357961071728256043309*x^37

+9498907763273239021574685*x^36+5622314253334154424175766*x^35

+3253035784774708879439262*x^34+1838319814003865364502115*x^33

+1013692519414068545966383*x^32+544883332503752228347324*x^31

+285189004474854548554157*x^30+145167679454737704278880*x^29

+71769782821380635837621*x^28+34412717940513453504180*x^27

+15977552472766155842750*x^26+7170548645642540233444*x^25

+3104565556800370034675*x^24+1293950334879519037064*x^23

+517913155627899876744*x^22+198540029295827265030*x^21

+72673216612249799707*x^20+25313244131813040492*x^19+8357520624415623570*x^18

+2603936594202983265*x^17+761697282842373791*x^16+207948182505922572*x^15

+52618101897021930*x^14+12239625173465375*x^13+2591895971809073*x^12

+493826644119635*x^11+83443844586997*x^10+12283604989433*x^9+1540197926928*x^8

+159778881431*x^7+13197261179*x^6+823860011*x^5

+36140317*x^4+1002806*x^3+15057*x^2+99*x+1)*(x-1)^3/((x^4-1)^5*(x^8-1)^2*(x^3-1)^5*(x^9-1)*(x^5-1)^4*(x^6-1)^6*(x^7-1)^3*(x^10-1)

EXAMPLE

For n = 1, there are a(1) = 96 order 6 permutation matrices with exactly one 1 in each of the two diagonals.

CROSSREFS

Cf. A111158.

Sequence in context: A189903 A189159 A254286 * A208443 A183418 A299950

Adjacent sequences:  A216036 A216037 A216038 * A216040 A216041 A216042

KEYWORD

nonn

AUTHOR

Guoce Xin, Aug 30 2012

STATUS

approved

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Last modified September 17 06:52 EDT 2019. Contains 327119 sequences. (Running on oeis4.)