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A228194 Sum of lengths of longest contiguous subsequences with the same value over all s in {1,...,n}^n. 4
0, 1, 6, 45, 436, 5345, 79716, 1403689, 28518736, 656835633, 16913175310, 481496895121, 15017297246832, 509223994442449, 18652724643726460, 733989868341011325, 30879549535458286096, 1383134389475750109089, 65714992805644764521724, 3300990246208225995520681 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

Project Euler, Problem 427: n-sequences

FORMULA

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

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

EXAMPLE

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

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);

CROSSREFS

Main diagonal of A228250.

Cf. A228618.

Sequence in context: A019577 A097814 A239910 * A084064 A186925 A294642

Adjacent sequences:  A228191 A228192 A228193 * A228195 A228196 A228197

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 17 2013

STATUS

approved

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Last modified October 22 00:52 EDT 2019. Contains 328315 sequences. (Running on oeis4.)