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A289354 Number of 9-digit numbers whose sum of digits is n. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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

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

EXAMPLE

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

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 *)

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).

Sequence in context: A008501 A341206 A306942 * A008491 A023034 A000581

Adjacent sequences:  A289351 A289352 A289353 * A289355 A289356 A289357

KEYWORD

base,fini,full,nonn

AUTHOR

Miquel Cerda, Jul 03 2017

STATUS

approved

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Last modified June 15 22:06 EDT 2021. Contains 345053 sequences. (Running on oeis4.)