A379181 a(n) is the number of n-digit nonnegative integers with mode and mean of the digits equal.
10, 9, 9, 237, 1617, 15099, 98490, 855675, 7020429, 68359815, 638064114, 6014495595, 55556308754, 504305784381, 4627364658702, 42696037939075, 402860074430853, 3847842858816523, 36989026236202050, 355682935667617515, 3396760984948340678, 32234267063991934093
Offset: 1
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..73
Programs
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Mathematica
a[n_]:=Module[{c=KroneckerDelta[n,1]}, For[k=10^(n-1), k<=10^n-1, k++, If[Commonest[IntegerDigits[k]]=={Mean[IntegerDigits[k]]}, c++]]; c]; Array[a,6] -
Python
from math import factorial, prod from collections import Counter from sympy.utilities.iterables import partitions def A379181(n): if n == 1: return 10 c, f = 0, factorial(n-1) for k in range(1,10): for s,p in partitions(k*n,m=n,k=9,size=True): v = list(p.values()) if n-s>0: p[0]=n-s r = Counter(p).most_common(2) if r[0][0]==k and (len(r)==1 or r[1][1]
Formula
Conjecture: a(n+1)/a(n) ~ 10. - Stefano Spezia, Jul 23 2025
Extensions
a(11)-a(22) from Chai Wah Wu, Dec 21 2024