login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001266 One-half the number of permutations of length n without rising or falling successions.
(Formerly M4426 N1871)
5
0, 0, 1, 7, 45, 323, 2621, 23811, 239653, 2648395, 31889517, 415641779, 5830753109, 87601592187, 1403439027805, 23883728565283, 430284458893701, 8181419271349931, 163730286973255373, 3440164703027845395, 75718273707281368117, 1742211593431076483419 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,4

COMMENTS

(1/2) times number of permutations of 12...n such that none of the following occur: 12, 23, ..., (n-1)n, 21, 32, ..., n(n-1).

REFERENCES

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 263.

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

Alois P. Heinz and Seiichi Manyama, Table of n, a(n) for n = 2..450 (first 199 terms from Alois P. Heinz)

J. Riordan, A recurrence for permutations without rising or falling successions, Ann. Math. Statist. 36 (1965), 708-710.

FORMULA

a(n) = A002464(n)/2.

(1/2) times coefficient of t^0 in S[n](t) defined in A002464.

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, 0)/2:

seq(a(n), n=2..25);  # Alois P. Heinz, Jan 11 2013

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]]]; a[n_] := Coefficient[S[n], t, 0]/2; Table[a[n], {n, 2, 25}] (* Jean-Fran├žois Alcover, Mar 24 2014, after Alois P. Heinz *)

CROSSREFS

Sequence A002464 divided by 2 for n >= 2. A diagonal of A010028.

Sequence in context: A103719 A134437 A018927 * A071971 A006680 A197796

Adjacent sequences:  A001263 A001264 A001265 * A001267 A001268 A001269

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 16 2001

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 19 20:48 EST 2018. Contains 299357 sequences. (Running on oeis4.)