A383305 a(n) is number of n-digit nonnegative integers whose difference between the largest and smallest digits is equal to the arithmetic mean of its digits.

1, 6, 39, 266, 1730, 11361, 74809, 494194, 3273132, 21730506, 144588345, 964050593, 6440655572, 43111601819, 289112380019, 1942335481170, 13072051432742, 88125501965430, 595077180675348, 4024698113281006, 27261843502415806, 184931926767687963, 1256249015578188517, 8545135121520262849, 58198759816476208605

Offset: 1

Author

Stefano Spezia, Apr 22 2025

Keywords

• nonn
• base

Crossrefs

Cf. A037904, A054054, A054055, A371383, A371384, A383304.

Programs

Mathematica

a[n_]:=Module[{c=KroneckerDelta[n,1]}, For[k=10^(n-1), k<=10^n, k++, If[Max[d=IntegerDigits[k]]-Min[d]==Mean[d], c++]]; c]; Array[a,7]

Python

def A383305(n):
    if n<=1: return n
    s={(k,k,k):1 for k in range(1,10)}
    for i in range(n-1):
        snew={}
        for (h,l,t),v in s.items():
            for d in range(10):
                p=(max(h,d),min(l,d),t+d)
                if p in snew:
                    snew[p]+=v
                else:
                    snew[p]=v
        s=snew
    return sum( v for (h,l,t),v in s.items() if n*(h-l)==t) # Bert Dobbelaere, Apr 25 2025

Extensions

More terms from Bert Dobbelaere, Apr 25 2025