The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A362596 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A362596

Number of parking functions of size n avoiding the patterns 213 and 321.
(history; published version)

#20 by R. J. Mathar at Thu Jan 11 09:10:04 EST 2024

STATUS

editing

approved

#19 by R. J. Mathar at Thu Jan 11 09:10:00 EST 2024

FORMULA

D-finite with recurrence 2*(n+1)*a(n) +2*(-15*n+1)*a(n-1) +(167*n-193)*a(n-2) +2*(-204*n+467)*a(n-3) +184*(2*n-7)*a(n-4)=0. - R. J. Mathar, Jan 11 2024

STATUS

approved

editing

#18 by Alois P. Heinz at Fri Apr 28 05:27:40 EDT 2023

STATUS

reviewed

approved

#17 by Joerg Arndt at Fri Apr 28 01:03:02 EDT 2023

STATUS

proposed

reviewed

#16 by Chai Wah Wu at Thu Apr 27 21:00:44 EDT 2023

STATUS

editing

proposed

#15 by Chai Wah Wu at Thu Apr 27 21:00:40 EDT 2023

PROG

(Python)

from math import comb

def A362596(n): return ((n*(n-3)+4)*comb(n<<1, n)//(n+1)>>2)+(1<<(n<<1)-3) if n>1 else 1 # Chai Wah Wu, Apr 27 2023

STATUS

approved

editing

#14 by Alois P. Heinz at Thu Apr 27 16:51:36 EDT 2023

STATUS

proposed

approved

#13 by Lara Pudwell at Thu Apr 27 16:49:34 EDT 2023

STATUS

editing

proposed

#12 by Lara Pudwell at Thu Apr 27 16:49:13 EDT 2023

DATA

1, 1, 3, 13, 60, 275, 1238, 5480, 23922, 103267, 441798, 1876366, 7921488, 33275758, 139194812, 580180598, 2410827422, 9990993443, 41308185542, 170439003998, 701953309592, 2886284314298, 11850433719572, 48591008205608, 199002198798980, 814117064956430

OFFSET

1,2

0,3

FORMULA

For n>=1, a(n) = (n^2 - 3*n + 4)/4*A000108(n) + 4^(n - 1)/2.

For n>=1, a(n) = A000108(n) + Sum_{m=1..n-1} m*A028364(n-1,m-1).

G.f.: 1+((9*x^2 - 10*x + 2)*sqrt(1 - 4*x) - 23*x^2 + 14*x - 2)/(2*(1 - 4*x)^(3/2)*x).

STATUS

proposed

editing

Discussion

Thu Apr 27

16:49

Lara Pudwell: Updated to include a(0)=1.

#11 by Andrew Howroyd at Thu Apr 27 10:13:43 EDT 2023

STATUS

editing

proposed