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!)
A307788 Number of valid hook configurations of permutations of [n] that avoid the patterns 231 and 321. 0
1, 1, 1, 2, 5, 12, 29, 72, 182, 466, 1207, 3158, 8334, 22158, 59299, 159614, 431838, 1173710, 3203244, 8774780, 24118522, 66497316, 183858411, 509670494, 1416231616, 3944027402, 11006186760, 30772507128, 86191006746, 241815195292 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Essentially the same as A217333 and A025273. - R. J. Mathar, May 17 2019

LINKS

Table of n, a(n) for n=0..29.

Colin Defant, Motzkin intervals and valid hook configurations, arXiv preprint arXiv:1904.10451 [math.CO], 2019.

FORMULA

G.f.: (1 - 2*x + 2*x^2 - sqrt(1 - 4*x + 4*x^2 - 4*x^3 + 4*x^4)) / (2*x^2).

D-finite with recurrence: (n+2)*a(n) +2*(-2*n-1)*a(n-1) +4*(n-1)*a(n-2) +2*(-2*n+5)*a(n-3) +4*(n-4)*a(n-4)=0. - R. J. Mathar, May 17 2019

PROG

(PARI) my(x='x+O('x^35)); Vec((1 - 2*x + 2*x^2 - sqrt(1 - 4*x + 4*x^2 - 4*x^3 + 4*x^4))/(2*x^2)) \\ Michel Marcus, May 08 2019

CROSSREFS

Cf. A307786, A307787.

Sequence in context: A122745 A166292 A010374 * A025273 A217333 A089372

Adjacent sequences:  A307785 A307786 A307787 * A307789 A307790 A307791

KEYWORD

nonn

AUTHOR

Colin Defant, Apr 28 2019

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 11 20:13 EDT 2022. Contains 356067 sequences. (Running on oeis4.)