|
| |
|
|
A031972
|
|
a(n) = Sum_{k=1..n} n^k.
|
|
10
|
|
|
|
0, 1, 6, 39, 340, 3905, 55986, 960799, 19173960, 435848049, 11111111110, 313842837671, 9726655034460, 328114698808273, 11966776581370170, 469172025408063615, 19676527011956855056, 878942778254232811937, 41660902667961039785742, 2088331858752553232964199
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Sum of lengths of longest ending contiguous subsequences with the same value over all s in {1,...,n}^n: a(n) = Sum_{k=1..n} k*A228273(n,k). a(2) = 6 = 2+1+1+2: [1,1], [1,2], [2,1], [2,2]. - Alois P. Heinz, Aug 19 2013
a(n) is the expected wait time to see the contiguous subword 11...1 (n copies of 1) over all infinite sequences on alphabet {1,2,...,n}. - Geoffrey Critzer, May 19 2014
a(n) is the number of sequences of k elements from {1,2,...,n}, where 1<=k<=n. For example, a(2) = 6, counting the sequences, [1], [2], [1,1], [1,2], [2,1], [2,2]. Equivalently, a(n) is the number of bar graphs having a height and width of at most n. - Emeric Deutsch, Jan 24 2017.
In base n, a(n) has n+1 digits: n 1's followed by a 0. - Mathew Englander, Oct 20 2020
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(1)=1; for n!=1 a(n) = (n^(n+1)-1)/(n-1) - 1. - Benoit Cloitre, Aug 17 2002
|
|
|
MAPLE
|
a:= n-> `if`(n<2, n, (n^(n+1)-n)/(n-1)):
|
|
|
MATHEMATICA
|
|
|
|
PROG
|
(Haskell)
a031972 n = sum $ take n $ iterate (* n) n
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
