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

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..73

Formula

Conjecture: a(n+1)/a(n) ~ 10. - Stefano Spezia, Jul 23 2025

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]

Prog

(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]<r[0][1]):
                w = prod((factorial(i) for i in v))*factorial(n-s)
                c += sum(f*i//w for i in v)
    return c # Chai Wah Wu, Dec 21 2024

Crossrefs

Cf. A378564, A378836, A379180.

Sequence in context: A070562 A216557 A382090 * A070641 A231471 A063661

Adjacent sequences: A379178 A379179 A379180 * A379182 A379183 A379184

Keyword

nonn,base

Author

Stefano Spezia, Dec 17 2024

Extensions

a(11)-a(22) from Chai Wah Wu, Dec 21 2024

Status

approved