A360538 Number of multisets of n nonzero digits such that sum(digits) > product(digits).

0, 0, 9, 10, 11, 12, 15, 16, 18, 20, 22, 23, 25, 26, 29, 30, 31, 32, 35, 36, 38, 39, 41, 42, 44, 44, 47, 50, 51, 52, 54, 55, 56, 57, 60, 60, 60, 61, 63, 64, 65, 67, 70, 71, 73, 73, 74, 75, 77, 77, 78, 80, 81, 82, 84, 85, 86, 87, 89, 90, 91, 92, 95, 96, 97, 98, 101, 101

Offset

0,3

Comments

Note that this does not represent the number of n-digit numbers that satisfy this property; that would require the computation of the permutations of each multiset.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Example

For n = 2, the a(2) = 9 solutions are [11,12,13,14,15,16,17,18,19].
For n = 3, the a(3) = 10 solutions are [111,112,113,114,115,116,117,118,119,122].

Maple

b:= proc(n, i, s, p) option remember; `if`(s+n*i<=p, 0,
     `if`(n=0, 1, add(b(n-1, j, s+j, p*j), j=1..i)))
    end:
a:= n-> b(n, 9, 0, 1):
seq(a(n), n=0..100);  # Alois P. Heinz, Feb 11 2023

Crossrefs

Cf. A052382, A360971, A360972.

Sequence in context: A129849 A274562 A258469 * A173147 A342145 A293761

Adjacent sequences: A360535 A360536 A360537 * A360539 A360540 A360541

Keyword

nonn,look,base

Author

Charles Bershatsky, Feb 10 2023

Status

approved