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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A321315 Number of permutations of [n] where the length of the longest increasing subsequence is larger than or equal to the length of the longest decreasing subsequence. 4
1, 1, 5, 14, 78, 488, 3161, 25092, 231428, 2299664, 24809824, 296046900, 3863542365, 54081895706, 806425921874, 12828011279528, 217574673205512, 3914918953508792, 74300528009315864, 1482219340166034896, 31035891175182089248, 681299189806864371412, 15649118660372502746968 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..80

Wikipedia, Longest increasing subsequence

FORMULA

a(n) = Sum_{k=0..n-1} A321316(n,k).

a(n) = A321313(n) + A321314(n).

MAPLE

h:= l-> (n-> add(i, i=l)!/mul(mul(1+l[i]-j+add(`if`(j>

    l[k], 0, 1), k=i+1..n), j=1..l[i]), i=1..n))(nops(l)):

f:= l-> `if`(l[1]>=nops(l), h(l)^2, 0):

g:= (n, i, l)-> `if`(n=0 or i=1, f([l[], 1$n]),

     g(n, i-1, l) +g(n-i, min(i, n-i), [l[], i])):

a:= n-> g(n$2, []):

seq(a(n), n=1..23);

CROSSREFS

Cf. A003316, A321313, A321314, A321316.

Sequence in context: A316611 A174939 A320800 * A203225 A308386 A198039

Adjacent sequences:  A321312 A321313 A321314 * A321316 A321317 A321318

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 03 2018

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 October 19 17:24 EDT 2021. Contains 348091 sequences. (Running on oeis4.)