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A360972
Number of n-digit zeroless numbers whose digit sum is larger than the product of all digits.
2
0, 0, 17, 28, 51, 91, 189, 302, 513, 985, 1461, 1904, 3155, 4616, 7211, 10236, 12709, 15573, 21463, 31161, 56306, 70904, 85570, 100626, 135203, 155951, 188059, 293887, 434106, 522755, 612837, 888740, 1013337, 1182809, 1559292, 1755888, 1971286, 2208087, 2491034
OFFSET
0,3
LINKS
FORMULA
a(n) = |{ k in { A052382 } : A055642(k) = n and A007953(k) > A007954(k) }|.
EXAMPLE
a(2) = 17: 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91.
a(3) = 28: 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 131, 141, 151, 161, 171, 181, 191, 211, 212, 221, 311, 411, 511, 611, 711, 811, 911.
a(4) = 51: 1111, 1112, 1113, 1114, ..., 6111, 7111, 8111, 9111.
MAPLE
b:= proc(n, i, s, p) option remember;
`if`(s+n*i<=p, 0, `if`(n=0 or i=1, 1/n!,
add(b(n-j, i-1, s+i*j, p*i^j)/j!, j=0..n)))
end:
a:= n-> b(n, 9, 0, 1)*n!:
seq(a(n), n=0..40);
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Alois P. Heinz, Feb 27 2023
STATUS
approved