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%I #35 Dec 20 2020 07:45:40
%S 0,1,6,45,436,5345,79716,1403689,28518736,656835633,16913175310,
%T 481496895121,15017297246832,509223994442449,18652724643726460,
%U 733989868341011325,30879549535458286096,1383134389475750109089,65714992805644764521724,3300990246208225995520681
%N Sum of lengths of longest contiguous subsequences with the same value over all s in {1,...,n}^n.
%H Alois P. Heinz, <a href="/A228194/b228194.txt">Table of n, a(n) for n = 0..200</a>
%H Project Euler, <a href="https://projecteuler.net/problem=427">Problem 427: n-sequences</a>
%F a(n) = Sum_{k=1..n} k*A228154(n,k).
%F a(n) ~ (2-exp(-1)) * n^n. - _Vaclav Kotesovec_, Sep 10 2014
%e a(2) = 6 = 2+1+1+2: [1,1], [1,2], [2,1], [2,2].
%p a:= proc(n) option remember; local b; b:=
%p proc(m, s, i) option remember; `if`(m>i or s>m, 0,
%p `if`(i=1, n, `if`(s=1, (n-1)*add(b(m, h, i-1), h=1..m),
%p b(m, s-1, i-1) +`if`(s=m, b(m-1, s-1, i-1), 0))))
%p end; forget(b);
%p add(m*add(b(m, s, n), s=1..m), m=1..n)
%p end:
%p seq(a(n), n=0..30);
%t 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}]];
%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Dec 20 2020, after _Alois P. Heinz_ *)
%Y Main diagonal of A228250.
%Y Cf. A228618.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 17 2013
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