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A228194
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Sum of lengths of longest contiguous subsequences with the same value over all s in {1,...,n}^n.
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4
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0, 1, 6, 45, 436, 5345, 79716, 1403689, 28518736, 656835633, 16913175310, 481496895121, 15017297246832, 509223994442449, 18652724643726460, 733989868341011325, 30879549535458286096, 1383134389475750109089, 65714992805644764521724, 3300990246208225995520681
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} k*A228154(n,k).
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EXAMPLE
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a(2) = 6 = 2+1+1+2: [1,1], [1,2], [2,1], [2,2].
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MAPLE
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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);
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MATHEMATICA
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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}]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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