(Python)
#From recurrence
def a(n, adict={0:0, 1:0, 2:0, 3:0, 4:2, 5:7}):
if n in adict:
return adict[n]
adict[n]=3*a(n-1)-a(n-2)-2*a(n-3)+a(n-4)-a(n-5)-2*a(n-6)
return adict[n]
(Python)
#Returns the actual list of valid subsets
def contains1101(n):
patterns=list()
for start in range (1, n-2):
s=set()
for i in range(4):
if (1, 1, 0, 1)[i]:
s.add(start+i)
patterns.append(s)
s=list()
for i in range(2, n+1):
for temptuple in comb(range(1, n+1), i):
tempset=set(temptuple)
for sub in patterns:
if sub <= tempset:
s.append(tempset)
break
return s
#Counts all such sets
def countcontains1101(n):
return len(contains1101(n))
(PARI) x='x+O('x^30); concat([0, 0, 0, 0], Vec(x^4*(2+x)/(1-3*x+x^2+2*x^3-x^4+x^5+2*x^6))) \\
G. C. Greubel, Jan 03 2018
(Magma) I:=[0, 0, 0, 0, 2, 7]; [n le 6 select I[n] else 3*Self(n-1) - Self(n-2)-2*Self(n-3)+Self(n-4)-Self(n-5)-2*Self(n-6): n in [0..30]]; //
G. C. Greubel, Jan 03 2018
