A228618 Sum of lengths of shortest runs with the same value over all s in {1,...,n}^n.

0, 1, 6, 33, 280, 3185, 46956, 824593, 16782872, 387446193, 10000154620, 285312472621, 8916105651300, 302875136889793, 11112007033351602, 437893891702463085, 18446744083262649616, 827240261951698484129, 39346408075791905146044, 1978419655663922695962061

Offset: 0

Author

Alois P. Heinz, Aug 27 2013

Keywords

• nonn

Examples

			a(3) = 33 = 3 + 12*1 + 3 + 12*1 + 3: [1,1,1], [1,1,2], [1,1,3], [1,2,1], [1,2,2], [1,2,3], [1,3,1], [1,3,2], [1,3,3], [2,1,1], [2,1,2], [2,1,3], [2,2,1], [2,2,2], [2,2,3], [2,3,1], [2,3,2], [2,3,3], [3,1,1], [3,1,2], [3,1,3], [3,2,1], [3,2,2], [3,2,3], [3,3,1], [3,3,2], [3,3,3].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..140

Crossrefs

Cf. A228194.

Formula

a(n) = Sum_{k=0..n} k*A228617(n,k).

a(n) ~ n^n. - Vaclav Kotesovec, Sep 06 2014