login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A322294 Number of permutations of [n] with exactly floor(n/2) rising or falling successions. 4
1, 1, 2, 4, 10, 48, 120, 888, 2198, 22120, 54304, 685368, 1674468, 25344480, 61736880, 1087931184, 2644978110, 53138966904, 129019925424, 2909014993080, 7056278570108, 176372774697856, 427516982398576, 11729862804913680, 28417031969575260, 848948339328178128 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..696

FORMULA

a(n) = A001100(n,floor(n/2)).

MAPLE

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-> coeff(S(n), t, floor(n/2)):

seq(a(n), n=0..30);

MATHEMATICA

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]]];

t[n_, k_] := Ceiling[Coefficient[s[n], t, k]];

a[n_] := t[n, Floor[n/2]];

a /@ Range[0, 30] (* Jean-Fran├žois Alcover, Sep 25 2019, after Alois P. Heinz *)

CROSSREFS

Bisections give A322295 (even part), A322295 (odd part).

Cf. A001100.

Sequence in context: A113208 A173488 A000613 * A053500 A214724 A326325

Adjacent sequences:  A322291 A322292 A322293 * A322295 A322296 A322297

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 02 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 25 08:27 EDT 2021. Contains 345453 sequences. (Running on oeis4.)