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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000507 Number of permutations of [n] with exactly 3 increasing runs of length at least 2.
(Formerly M5323 N2314)
3
61, 1385, 19028, 206276, 1949762, 16889786, 137963364, 1081702420, 8236142455, 61386982075, 450403628440, 3266265481144, 23480284103492, 167687984079924, 1191656966048088, 8436830209386360, 59563995267159825, 419628657826253805 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,1

REFERENCES

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 260.

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

Table of n, a(n) for n=6..23.

FORMULA

a(n) = (3*7^n-(6*n-9)*5^n+(6*n^2-18*n+3)*3^n-4*n^3+18*n^2-8*n-15)/192.

MATHEMATICA

t[n_, 0] = 1; t[n_, k_] /; k > n/2 = 0; t[n_, k_] /; k <= n/2 := t[n, k] = (2k+1) t[n-1, k] + (n-2k+1) t[n-1, k-1]; a[n_] := t[n, 3]; Table[a[n], {n, 6, 23}] (* Jean-François Alcover, Feb 09 2016 *)

PROG

(MAGMA) [(3*7^n-(6*n-9)*5^n+(6*n^2-18*n+3)*3^n-4*n^3+18*n^2-8*n-15)/192: n in [6..30]]; // Vincenzo Librandi, Feb 09 2016

CROSSREFS

From Johannes W. Meijer, May 24 2009: (Start)

The a(n) sequence equals the fourth left hand column of A008971.

The a(2*n) sequence equals the fourth left hand column of A160486.

(End)

Sequence in context: A154428 A262017 A060061 * A143011 A211213 A229667

Adjacent sequences:  A000504 A000505 A000506 * A000508 A000509 A000510

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Definition changed for clarity and for consistency with A008971, and formula and additional terms added by Jon E. Schoenfield, Mar 26 2010

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 December 4 15:36 EST 2021. Contains 349526 sequences. (Running on oeis4.)