A336433 Number of sequences of n numbers from 1 to n that do not have a subsequence that adds up to n.

0, 0, 0, 1, 5, 68, 403, 7257, 61686, 1174434, 13810620, 335547727, 3783688286, 124486381056, 1935430229612, 55798127869680, 1058567311736669, 39819079382937334, 717447490866241055, 32064848897165970340, 666062878027691348450, 28916070816360797805534

Offset

0,5

Comments

The sequence is bounded above for odd n by (((n-1)/2)^n)*(2^((n-1)/2)).

Growth appears to be slightly faster than exponential, but irregular, with odd-numbered terms larger than the trend.

Links

Christopher L. Reedy, Table of n, a(n) for n = 1..30

Pierre Abbat, Fullproc

Christopher L. Reedy, sequence.py

Example

For n=3, the only solution is 2,2,2.
For n=4, the 5 solutions are 3,3,3,3 and the four permutations of 3,3,3,2.

Prog

(C++) See Fullproc link.
(Python) # See sequence.py link.

Crossrefs

Cf. A000312.

Sequence in context: A328359 A003361 A363401 * A099334 A281558 A165396

Adjacent sequences: A336430 A336431 A336432 * A336434 A336435 A336436

Keyword

nonn

Author

Pierre Abbat, Jul 21 2020

Extensions

a(19)-a(21) from Christopher L. Reedy, Aug 06 2020

Status

approved