A078266 Integer part of the arithmetic mean of all the distinct numbers formed by permuting the digits of concatenation of numbers from 1 to n.
1, 16, 222, 2777, 33333, 388888, 4444444, 49999999, 555555555, 46464646464, 4102564102563, 377777777777777, 35947712418300653, 3508771929824561403, 349206349206349206348, 35265700483091787439613, 3599999999999999999999999
Offset: 1
Examples
a(3) = floor((123 + 132 + 213 + 231 + 312 + 321)/6) = 222; a(4) = floor((1234 + 1243 + 1324 + 1342 + 1423 + 1432 + ... + 4312 + 4321)/24) = 66660/24 = 2777.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..369
Programs
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Maple
a:= proc(n) local s, t, l; s:= cat("", seq(i, i=1..n)); t:= length(s); l:= (p-> seq(coeff(p, x, i), i=0..9))(add(x^parse(s[i]), i=1..t)); floor((10^t-1)/9*add(i*l[i+1], i=1..9)/t) end: seq(a(n), n=1..20); # Alois P. Heinz, Jan 05 2019 -
PARI
{ a(n) = c=vector(10); for(i=1,n, s=eval(Vec(Str(i))); for(j=1,#s,c[s[j]+1]++); ); l=sum(j=1,10,c[j]); (10^l-1)/9*sum(j=1,10,(j-1)*c[j])\l } \\ Max Alekseyev -
Python
def A078266(n): s = ''.join(str(i) for i in range(1,n+1)) return sum(int(d) for d in s)*(10**len(s)-1)//(9*len(s)) # Chai Wah Wu, Jan 04 2019
Formula
Extensions
More terms from Max Alekseyev, Jan 24 2012
Comments