A278969 Number of 7-digit numbers whose sum of digits is n.

1, 7, 28, 84, 210, 462, 924, 1716, 3003, 5004, 7995, 12306, 18312, 26418, 37038, 50568, 67353, 87648, 111573, 139068, 169863, 203463, 239148, 275988, 312873, 348558, 381723, 411048, 435303, 453438, 464653, 468448, 464653, 453438, 435303, 411048, 381723, 348558, 312873, 275988, 239148, 203463, 169863, 139068, 111573, 87648, 67353, 50568, 37038, 26418, 18312, 12306, 7995, 5004, 3003, 1716, 924, 462, 210, 84, 28, 7, 1

Offset

1,2

Comments

There are 9000000 numbers with 7 decimal digits, the smallest being 1000000 and the largest 9999999.

Differs for n >= 10 (5004 vs 5005) from A000579(n+5) = binomial(n+5,6). - M. F. Hasler, Mar 05 2017

Links

Table of n, a(n) for n=1..63.

Formula

G.f.: (x - x^10)/(1 - x)*((1 - x^10)/(1 - x))^6. - Michael De Vlieger, Dec 07 2016

a(64-n) = a(n), 1 <= n <= 63. - M. F. Hasler, Mar 05 2017

Example

a(2)=7: 1000001, 1000010, 1000100, 1001000, 1010000, 1100000, 2000000.

Mathematica

Rest@ CoefficientList[Series[(x - x^10)/(1 - x) ((1 - x^10)/(1 - x))^#, {x, 0, 9 (# + 1)}], x] &@ 6 (* or *)
Function[w, Count[w, #] & /@ Range[Max@ w]]@ Map[Total@ IntegerDigits@ # &, Range[10^#, 10^(# + 1) - 1]] &@ 6 (* Michael De Vlieger, Dec 07 2016 *)

Prog

(PARI) b=vector(63, i, 0); for(n=1000000, 9999999, a=eval(Vec(Str(n))); b[sum(j=1, 7, a[j])]++); for(n=1, 63, print1(b[n], ", "))
(PARI) Vec((1-x^9)*(1-x^10)^6/(1-x)^7) \\ shorter than (1-x^9)/(1-x)*((1-x^10)/(1-x))^6, but not better. - M. F. Hasler, Mar 05 2017

Crossrefs

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

Sequence in context: A008489 A023032 A341204 * A000579 A290994 A049017

Adjacent sequences: A278966 A278967 A278968 * A278970 A278971 A278972

Keyword

base,fini,full,nonn,easy

Author

Daniel Mondot, Dec 02 2016

Status

approved