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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A307789 Number of valid hook configurations of permutations of [n] that avoid the patterns 231 and 1243. 1

%I

%S 1,1,1,2,5,13,35,96,267,750,2123,6046,17303,49721,143365,414584,

%T 1201917,3492117,10165779,29643870,86574831,253188111,741365049,

%U 2173243128,6377181825,18730782252,55062586341,161995031226,476941691177,1405155255055

%N Number of valid hook configurations of permutations of [n] that avoid the patterns 231 and 1243.

%C Essentially the same as A005773. - _R. J. Mathar_, May 06 2019

%H Colin Defant, <a href="http://arxiv.org/abs/1904.10451">Motzkin intervals and valid hook configurations</a>, arXiv preprint arXiv:1904.10451 [math.CO], 2019.

%F G.f.: 1 + 2*x^2/(3*x - 1 + sqrt(1 - 2*x - 3*x^2)).

%F D-finite with recurrence: +(-n+1)*a(n) +2*(n-1)*a(n-1) +3*(n-3)*a(n-2)=0. - _R. J. Mathar_, Jan 27 2020

%F a(n) = Sum_{k=0..n-2} A064189(n-2,k) for n>=2. - _Alois P. Heinz_, Aug 29 2022

%Y Cf. A005773, A064189.

%K nonn

%O 0,4

%A _Colin Defant_, Apr 28 2019

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 1 01:28 EDT 2022. Contains 357134 sequences. (Running on oeis4.)