A360538 - OEIS

%I #43 Feb 27 2023 15:28:18

%S 0,0,9,10,11,12,15,16,18,20,22,23,25,26,29,30,31,32,35,36,38,39,41,42,

%T 44,44,47,50,51,52,54,55,56,57,60,60,60,61,63,64,65,67,70,71,73,73,74,

%U 75,77,77,78,80,81,82,84,85,86,87,89,90,91,92,95,96,97,98,101,101

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

%C 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.

%H Alois P. Heinz, <a href="/A360538/b360538.txt">Table of n, a(n) for n = 0..10000</a>

%e For n = 2, the a(2) = 9 solutions are [11,12,13,14,15,16,17,18,19].

%e For n = 3, the a(3) = 10 solutions are [111,112,113,114,115,116,117,118,119,122].

%p b:= proc(n, i, s, p) option remember; `if`(s+n*i<=p, 0,

%p      `if`(n=0, 1, add(b(n-1, j, s+j, p*j), j=1..i)))

%p     end:

%p a:= n-> b(n, 9, 0, 1):

%p seq(a(n), n=0..100);  # _Alois P. Heinz_, Feb 11 2023

%Y Cf. A052382, A360971, A360972.

%K nonn,look,base

%O 0,3

%A _Charles Bershatsky_, Feb 10 2023