ez:=proc(): print(`M(d), C(N) `): end:

with(linalg):

M:=proc(d) local T,a,b:

for a from 1 to 2*d do
for b from 1 to d do

if a=2*b then
 T[a,2*b-1]:=1:
elif b=(a-1)/3 and a>=4 then
 T[a,2*b-1]:=-1:
else
T[a,2*b-1]:=0:
fi:

if b=(a+1)/2 then
 T[a,2*b]:=1 :
elif b=a+1 then
 T[a,2*b]:=-1:
else
 T[a,2*b]:=0:
fi:

od:
od:


[seq([seq(T[a,b],b=1..2*d)],a=1..2*d)]:

end:

#C(N): checks the conjecture that det(Mat1(n))=(-1)^n for n from 1 to N, try
#C(10);
C:=proc(N) local i:
evalb({seq(det(M(i))-(-1)^i,i=1..N)}={0}):
end: