A360972 - OEIS

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A360972

Number of n-digit zeroless numbers whose digit sum is larger than the product of all digits.

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

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OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

Cf. A007953, A007954, A052382, A055642, A360538.

Sequence in context: A032611 A255200 A350101 * A319265 A238572 A266965

Adjacent sequences: A360969 A360970 A360971 * A360973 A360974 A360975

KEYWORD

nonn,base

AUTHOR

Alois P. Heinz, Feb 27 2023

STATUS

approved