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A086855
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Number of permutations of length n with exactly 4 rising or falling successions.
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3
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0, 0, 0, 0, 0, 2, 22, 226, 2198, 22120, 236968, 2732268, 33940644, 453148422, 6480322210, 98907371822, 1605581578202, 27631315113916, 502618772515748, 9637245372790760, 194291040277517688, 4109014039030693578, 90968013940830446574, 2104072961763468757082
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OFFSET
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0,6
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COMMENTS
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Permutations of 12...n such that exactly 4 of the following occur: 12, 23, ..., (n-1)n, 21, 32, ..., n(n-1).
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REFERENCES
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F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 263.
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LINKS
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FORMULA
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Coefficient of t^4 in S[n](t) defined in A002464.
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MAPLE
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S:= proc(n) option remember; `if`(n<4, [1, 1, 2*t, 4*t+2*t^2]
[n+1], expand((n+1-t)*S(n-1) -(1-t)*(n-2+3*t)*S(n-2)
-(1-t)^2*(n-5+t)*S(n-3) +(1-t)^3*(n-3)*S(n-4)))
end:
a:= n-> ceil(coeff(S(n), t, 4)):
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MATHEMATICA
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S[n_] := S[n] = If[n<4, {1, 1, 2*t, 4*t+2*t^2}[[n+1]], Expand[(n+1-t)*S[n-1] - (1-t)*(n-2+3*t)*S[n-2] - (1-t)^2*(n-5+t)*S[n-3] + (1-t)^3*(n-3)*S[n-4]]]; a[n_] := Ceiling[Coefficient[S[n], t, 4]]; Table [a[n], {n, 0, 25}] (* Jean-François Alcover, Oct 13 2014, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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