A289354 Number of 9-digit numbers whose sum of digits is n.

1, 9, 45, 165, 495, 1287, 3003, 6435, 12870, 24309, 43741, 75465, 125445, 201675, 314523, 477015, 705012, 1017225, 1435005, 1981845, 2682559, 3562131, 4644255, 5949615, 7493982, 9286233, 11326425, 13604085, 16096905, 18770031, 21576079, 24455955, 27340500, 30152925, 32811945, 35235465, 37344615, 39067875, 40344975, 41130255, 41395240, 41130255, 40344975, 39067875, 37344615, 35235465, 32811945, 30152925, 27340500, 24455955, 21576079, 18770031, 16096905, 13604085, 11326425, 9286233, 7493982, 5949615, 4644255, 3562131, 2682559, 1981845, 1435005, 1017225, 705012, 477015, 314523, 201675, 125445, 75465, 43741, 24309, 12870, 6432, 3003, 1287, 495, 165, 45, 9, 1

Offset: 1

Author

Miquel Cerda, Jul 03 2017

Keywords

• base
• fini
• full
• nonn

Comments

There are 900000000 numbers with 9 decimal digits, the smallest being 100000000 and the largest 999999999.

Examples

			a(2)=9: 100000001, 100000010, 100000100, 100001000, 100010000, 100100000, 101000000, 11000000, 20000000.
		

Links

• Miquel Cerda, Table of n, a(n) for n = 1..81

Crossrefs

Cf. A071817 (3-digit numbers), A090579 (4-digit numbers), A090580 (5-digit numbers), A090581 (6-digit numbers), A278969 (7-digit numbers), A278971 (8-digit numbers).

Programs

Mathematica

With[{d = 9}, Rest@ CoefficientList[Series[(x - x^10)/(1 - x) ((1 - x^10)/(1 - x))^(d - 1), {x, 0, 9 d}], x]] (* Michael De Vlieger, Jul 04 2017 *)

Formula

a(n) = a(82 - n). - David A. Corneth, Jul 03 2017

G.f.: (x - x^10)/(1 - x)*((1 - x^10)/(1 - x))^8 - Michael De Vlieger, Jul 04 2017