A068595 Number of functions from {1,2,...,n} to {1,2,...,n} such that the sum of the function values is 0 mod 3.

0, 2, 9, 85, 1041, 15552, 274514, 5592406, 129140163, 3333333333, 95103890203, 2972033482752, 100958368864084, 3704002275186006, 145964630126953125, 6148914691236517205, 275746753962112254725, 13115469358432179191808, 659473218553437863041326, 34952533333333333333333334

Offset

1,2

Comments

If the functions counted are those whose sum of values is 0 mod 2 (instead of 0 mod 3) it appears that we get A057065.

It appears that a(n) = floor((n^n)/3) for n>2.

This conjecture is false for n=8, n=14, and n=20. - Sean A. Irvine, Feb 26 2024

Links

Table of n, a(n) for n=1..20.

Sean A. Irvine, Java program (github)

sci.math thread [Broken link?]

Crossrefs

Cf. A057065.

Sequence in context: A262011 A120959 A125797 * A330475 A356615 A037172

Adjacent sequences: A068592 A068593 A068594 * A068596 A068597 A068598

Keyword

nonn

Author

John W. Layman, Mar 13 2002

Extensions

a(9)-a(20) from Sean A. Irvine, Feb 26 2024

Status

approved