The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A186735 Number of permutations of [n] with no ascending runs of length 1 or 2. 2
 1, 0, 0, 1, 1, 1, 20, 69, 180, 1930, 12611, 61051, 566129, 5179750, 38348469, 376547340, 4169246332, 41559058969, 465750294781, 5905176350849, 72848728572828, 946103621115633, 13501160406995728, 195518567272213262, 2918439778172724571, 46559546190633191495 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..150 FORMULA a(n) = A000142(n) - A228614(n) - A185652(n). EXAMPLE a(0) = 1: the empty permutation. a(3) = 1: 123. a(4) = 1: 1234. a(5) = 1: 12345. a(6) = 20: 123456, 124356, 125346, 126345, 134256, 135246, 136245, 145236, 146235, 156234, 234156, 235146, 236145, 245136, 246135, 256134, 345126, 346125, 356124, 456123. MATHEMATICA A[n_, k_] := A[n, k] = Module[{b}, b[u_, o_, t_] := b[u, o, t] = If[t + o <= k, (u + o)!, Sum[b[u + i - 1, o - i, Min[k, t] + 1], {i, 1, o}] + If[t <= k, u*(u + o - 1)!, Sum[b[u - i, o + i - 1, 1], {i, 1, u}]]]; Sum[b[j - 1, n - j, 1], {j, 1, n}]]; a[n_] := n! - A[n, 2]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Sep 03 2021, after Alois P. Heinz in A064315 *) CROSSREFS Cf. A064315, A097899. Cf. A000142, A185652, A228614. Sequence in context: A044158 A044539 A297597 * A363840 A238101 A153728 Adjacent sequences: A186732 A186733 A186734 * A186736 A186737 A186738 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 29 2013 STATUS approved

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

Last modified April 17 11:12 EDT 2024. Contains 371763 sequences. (Running on oeis4.)