A289380 Number of 10-digit numbers whose sum of digits is n.

1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 48619, 92359, 167815, 293215, 494725, 808753, 1284481, 1986490, 2997280, 4419415, 6376951, 9015769, 12502435, 17021245, 22769185, 29948644, 38757862, 49379275, 61966135, 76628035, 93416221, 112309741, 133203565, 155899810, 180103120

Offset: 1

Author

Miquel Cerda, Jul 04 2017

Keywords

• base
• fini
• full
• nonn

Comments

The 10-digit numbers distributed according to the sum of their digits n.

The sequence is symmetrical; a(n) = a(91 - n), 1 <= n <= 91.

Examples

			a(2)=10: 1000000001, 1000000010, 1000000100, 1000001000, 1000010000, 1000100000, 1001000000, 1010000000, 110000000, 200000000.
		

Links

• Miquel Cerda, Table of n, a(n) for n = 1..90

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), A289354 (9-digit numbers).

Programs

Mathematica

CoefficientList[Series[(1 - x^10)^9*(1 - x^9)/(1 - x)^10, {x, 0, 40}],
x] (* Wesley Ivan Hurt, Jul 09 2017 *)

Formula

G.f.: (1 - x^10)^9*(x - x^10)/(1 - x)^10.