BEIN&  THE  FIEST  CLASS  OF  E-GONOUS  X-EDEA. 
159 
33=  {R“»(5, 1).E^'"“(5,0)+R®“"(5,0).R““(5, 1)+E“«(5,  2}  0)+Il”*“(5,2}  R^“*"(5,0)} 
+ 1)  1)+R“'’(5, 2)  R’"'’(6, 1)+R^'“(5, 1)  R“‘'(5,  2)+R“"(5, 2)  R"-(5,  2)} 
x!i(2+j^)-N.,,-N,, 
= {1.1  + 1. 1 + 1. 1 + 1. 1>1  + {1.1  + 1. 1+1. 1 + 1. 1}3=16. 
For  365  the  partitions  of  the  6-pyramid,  we  have  the  following  partitions  of  the  hex- 
gon 
R6«^.{^6,0)=1,  R^“^"':(6,l)=l,  R"*(6,l)=l, 
R2ag.{^0^2)=:l,  R‘^'(6,2)  =1,  1(6,2)  =1, 
R^t6,3)=l,  P(6,3)=l, 
R^'^‘(6,  3)=1; 
wherefore  the  formula  of  XVIII.  becomes, 
06  = 198,  thus: 
36=  0).R‘^'(6, 1-f  6,  2+6,  3)+R«''^'^^(6,  0).R®'(6, 1+6, 2+6,  3)}.!i(^2+^)  [=  6] 
+ {R2AeD{(6,l+6,2).R«“^'^'(6,0)+R^“^'''(6,l+6,2)  R®^^°'(6,  0)}.!i(^2+^)  [=  4] 
+ {R2AcDi(6,i+6,2).R'^'(6,l  + 6,2  + 6,  3)+R^“^'^'(6, 1 + 6,  2).R^^(6,l  + 6,2  + 6,  3)}.+(^2+|j-)  [=24] 
+ {R^^'^°'(6, 1+6,  2).R-^<^'(6, 1 + 6,  2)}!i(2+^)  [=  8] 
+ {R^^(6, 1+6,  2 + 6,  3).R<^'(6, 1 + 6,  2+6,  3)}.^  ^ [=27] 
+ {R6AcD,(6,  0).R3<^'(6,  3)+R6“^'''(6,  0).R3D'(6,  3)}.!i(^2+^)  [=  2] 
+ {R2AoD{(6,  2).R^‘''(6,  3)+R^“^'^'(6, 1+6,  2}.R^°'(6,  3)}.!i(^2+^)  [=  4] 
+ {R°'(6, 1+6,  2+6,  3).R^'^'(6,  3)+R‘^'(6, 1+6,  2 + 6,  3).R^^‘(6,  3)}- [=  6] 
+R*°^(6,  3).R^‘^'(6,  3)i3|+I(6,  2)1(6,  2).2.j^+P(6,  3)P(6,  3). 2-^  [=19] 
+ {R«^^°'(6,  0)1(6,  2)+R«“^'''(6,  0)1(6,  2)}.^^  [=  2] 
+ {R«^^>^'(6,  0)P(6,  3)+R«“^‘^'(6,  0)P(6,  3)}.^  [=  2] 
+ {R2AcD.(6,  i_|_e^  2)1(6,  2)+R^“^'''(6, 1+6,  2). 1(6,2)}^  [=12] 
+ {R2AcD{(6,  2)P(6,  3)+R^“^^'(6,  1+6,  2)P(6,  3)}.^  [=12] 
+ {R°‘(6, 1+6,  2 + 6,  3). 1(6,  2)  + R<''(6, 1+6,  2 + 6,  3)1(6,  2)}.  [=36] 
