OFFSET
1,1
COMMENTS
Clauses are multisets of 3 literals chosen from {x_1, ..., x_n, not x_1, ..., not x_n}; repeated literals inside a clause are allowed. A formula is a multiset of 3 such clauses, so repeated clauses are also allowed.
This is the m=3 column of A396351.
REFERENCES
Stephen A. Cook, The complexity of theorem-proving procedures, Proceedings of the Third Annual ACM Symposium on Theory of Computing, 1971, 151-158.
LINKS
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 2*n*(2*n^3 + 3*n^2 + 19*n - 18)/3.
From Stefano Spezia, May 24 2026: (Start)
G.f.: 4*x*(1 + 11*x - 10*x^2 + 6*x^3)/(1 - x)^5.
E.g.f.: 2*exp(x)*x*(6 + 42*x + 15*x^2 + 2*x^3)/3. (End)
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {4, 64, 240, 624, 1340}, 36] (* Stefano Spezia, May 24 2026 *)
PROG
(Python)
def a(n):
return 2*n*(2*n**3 + 3*n**2 + 19*n - 18)//3
print([a(n) for n in range(1, 37)])
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ramin Mohammadi Masoudi, May 23 2026
STATUS
approved