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 A001251 Number of permutations of order n with the length of longest run equal 3. (Formerly M2031 N0803) 12
 0, 0, 2, 12, 70, 442, 3108, 24216, 208586, 1972904, 20373338, 228346522, 2763212980, 35926266244, 499676669254, 7405014187564, 116511984902094, 1940073930857802, 34087525861589564, 630296344519286304, 12235215845125112122, 248789737587365945992 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 262. (Terms for n>=13 are incorrect). N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Max Alekseyev and Alois P. Heinz, Table of n, a(n) for n = 1..450 (first 100 terms from Max Alekseyev) Max A. Alekseyev, On the number of permutations with bounded runs length, arXiv preprint arXiv:1205.4581 [math.CO], 2012-2013. - From N. J. A. Sloane, Oct 23 2012 Richard Ehrenborg and JiYoon Jung, Descent pattern avoidance, arXiv preprint:1312.2027 [math.CO], 6 Dec 2013. FORMULA a(n) ~ c * d^n * n!, where d = 0.92403585760753647721113386869798700855648617941... is the root of the equation 8 - 2*sin(sqrt(phi)/d) * (2*sqrt(5*(phi-1)) * cosh(sqrt(phi-1)/d) + 2*sinh(sqrt(phi-1)/d)) + 2*cos(sqrt(phi)/d) * (6*cosh(sqrt(phi-1)/d) + 2*sqrt(5*phi) * sinh(sqrt(phi-1)/d)) = 0, phi = A001622 = (1+sqrt(5))/2 is the golden ratio and c = 1.259371257828351725264434486385284120241474052544197367866029465830756911... - Vaclav Kotesovec, Sep 06 2014, updated Aug 18 2018 MATHEMATICA length = 3; g[u_, o_, t_] := g[u, o, t] = If[u+o == 0, 1, Sum[g[o + j - 1, u - j, 2], {j, 1, u}] + If[t

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Last modified July 24 23:25 EDT 2021. Contains 346273 sequences. (Running on oeis4.)