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

1,2

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.

Links

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

Formula

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

Example

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

Mathematica

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

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).

Sequence in context: A341139 A070212 A341207 * A008502 A008492 A023035

Adjacent sequences: A289377 A289378 A289379 * A289381 A289382 A289383

Keyword

base,fini,full,nonn

Author

Miquel Cerda, Jul 04 2017

Status

approved