A228194 Sum of lengths of longest contiguous subsequences with the same value over all s in {1,...,n}^n.

0, 1, 6, 45, 436, 5345, 79716, 1403689, 28518736, 656835633, 16913175310, 481496895121, 15017297246832, 509223994442449, 18652724643726460, 733989868341011325, 30879549535458286096, 1383134389475750109089, 65714992805644764521724, 3300990246208225995520681

Offset: 0

Author

Alois P. Heinz, Aug 17 2013

Keywords

• nonn

Examples

			a(2) = 6 = 2+1+1+2: [1,1], [1,2], [2,1], [2,2].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200
• Project Euler, Problem 427: n-sequences

Crossrefs

Main diagonal of A228250.

Cf. A228618.

Programs

Maple

a:= proc(n) option remember; local b; b:=
      proc(m, s, i) option remember; `if`(m>i or s>m, 0,
       `if`(i=1, n, `if`(s=1, (n-1)*add(b(m, h, i-1), h=1..m),
        b(m, s-1, i-1) +`if`(s=m, b(m-1, s-1, i-1), 0))))
      end; forget(b);
      add(m*add(b(m, s, n), s=1..m), m=1..n)
    end:
seq(a(n), n=0..30);

Mathematica

a[n_] := a[n] = Module[{b}, b[m_, s_, i_] := b[m, s, i] = If[m>i || s>m, 0, If[i==1, n, If[s==1, (n-1) Sum[b[m, h, i-1], {h, 1, m}], b[m, s-1, i-1] + If[s==m, b[m-1, s-1, i-1], 0]]]]; Sum[m Sum[b[m, s, n], {s, 1, m}], {m, 1, n}]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz *)

Formula

a(n) = Sum_{k=1..n} k*A228154(n,k).

a(n) ~ (2-exp(-1)) * n^n. - Vaclav Kotesovec, Sep 10 2014