A071817 Number of 3-digit numbers whose digits add up to n.

1, 3, 6, 10, 15, 21, 28, 36, 45, 54, 61, 66, 69, 70, 69, 66, 61, 54, 45, 36, 28, 21, 15, 10, 6, 3, 1

Offset

1,2

Comments

The sequence as a whole is palindromic; a(n) = a(28-n). - Jon E. Schoenfield, Nov 19 2016

Links

Table of n, a(n) for n=1..27.

Formula

G.f.: (1 - x^10)^2*(x - x^10)/(1 - x)^3. - Miquel Cerda, Jul 09 2017

Example

a(4) = 10 because there are 10 different 3-digit numbers whose digit sum is 4 (103, 112, 121, 130, 202, 211, 220, 301, 310, 400, which are the 3-digit elements of A052218).

Maple

for i from 1 to 9*3 do a[i] := 0:od:for i from 100 to 999 dob := convert(i, base, 10): s := sum(b[j], j=1..nops(b)):a[s] := a[s]+1:od:seq(a[j], j=1..3*9);

Crossrefs

Cf. A071816.

Sequence in context: A062918 A113168 A341192 * A033442 A105335 A130489

Adjacent sequences: A071814 A071815 A071816 * A071818 A071819 A071820

Keyword

fini,full,nonn,base

Author

Graeme McRae, Jun 07 2002

Extensions

Corrected and extended by Sascha Kurz, Feb 07 2003

Name clarified by Jon E. Schoenfield, Nov 20 2016

Status

approved