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

1,2

Links

Table of n, a(n) for n=1..25.

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]

Prog

(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

Crossrefs

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

Sequence in context: A052392 A370376 A388409 * A357206 A386843 A370026

Adjacent sequences: A383302 A383303 A383304 * A383306 A383307 A383308

Keyword

nonn,base

Author

Stefano Spezia, Apr 22 2025

Extensions

More terms from Bert Dobbelaere, Apr 25 2025

Status

approved