A357030 a(n) is the number of integers in 0..n having nonincreasing digits.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 17, 18, 19, 19, 19, 19, 19, 19, 19, 20, 21, 22, 23, 24, 24, 24, 24, 24, 24, 25, 26, 27, 28, 29, 30, 30, 30, 30, 30, 31, 32, 33, 34, 35, 36, 37, 37, 37, 37, 38, 39, 40
Offset: 0
Examples
a(20) = 13 because there are 13 numbers in 0..20 whose digits are in nonincreasing order: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20.
Crossrefs
Cf. A009996.
Programs
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Maple
a:= proc(n) option remember; `if`(n<0, 0, a(n-1)+`if`( (l-> is(l=sort(l)))(convert(n, base, 10)), 1, 0)) end: seq(a(n), n=0..72); # Alois P. Heinz, Sep 12 2022 -
Mathematica
Accumulate @ Table[If[GreaterEqual @@ IntegerDigits[n], 1, 0], {n, 0, 72}] (* Amiram Eldar, Sep 10 2022 *) -
PARI
a(n) = sum(k=0, n, my(d=digits(k)); d == vecsort(d,,4)); \\ Michel Marcus, Sep 10 2022