#OK to post homework
#Tianyi Liu, Nov1, Assignment 15
1. 
RoG:=proc(k,n) local V,E,i,j,T1,v,Neighs,Moves,m,pt,a,b,c,d:

V:=[seq(seq(seq([i,j],j=1..n),i=1..k))]:


for i from 1 to nops(V) do
T1[V[i]]:=i:
od:


E:=[]:

for i from 1 to nops(V) do
 pt:=V[i]:

Moves:={}:

for a from 1 to k do
 Moves:={[a,0]} union Moves:
od:
for b from 1 to k do
 Moves:={[-a,0]} union Moves:
od:
for c from 1 to n do
 Moves:={[0,c]} union Moves:
od:
for d from 1 to n do
 Moves:={[0,-d]} union Moves:
od:

Neighs:={seq(pt+m,m in Moves)}:

Neighs:=Neighs intersect convert(V,set):

E:=[op(E),{seq(T1[v],v in Neighs)}]:
od:

E,V:
end:

seq(SAWnu(RoG(3,n)[1]),n=1..6)
1, 0, 2, 48, 2592, 276480


2.
NuW([40,40],A)
2382564832244243056285491057263
NuGW([40,40],A)
89322096703094945357683861273

Paths that never go above x=y:
2293242735541148110927807195990

SeqGW({[1,0,0],[0,1,0],[0,0,1],[1,1,1]},20)
[2, 10, 88, 1043, 14778, 236001, 4107925, 76314975, 1491934038, 30389576308, 640286048416, 13877540824735, 308102204007536, 6983346070924707, 161156356282624227, 3778249609096250059, 89826197363219012470, 2162338803354415120414, 52637415804379149938876, 1294313658632145337351381]