A090581 Number of numbers with 6 decimal digits and sum of digits = n.

1, 6, 21, 56, 126, 252, 462, 792, 1287, 2001, 2992, 4317, 6027, 8162, 10746, 13782, 17247, 21087, 25212, 29496, 33787, 37917, 41712, 45002, 47631, 49467, 50412, 50412, 49467, 47631, 45002, 41712, 37917, 33787, 29496, 25212, 21087, 17247, 13782, 10746, 8162, 6027, 4317, 2992, 2001, 1287, 792, 462, 252, 126, 56, 21, 6, 1

Offset

1,2

Comments

There are 900000 6-digit numbers, the smallest being 100000 and the largest 999999.

Links

Table of n, a(n) for n=1..54.

Formula

G.f.: (x - x^10)/(1 - x)*((1 - x^10)/(1 - x))^5. - Michael De Vlieger, Dec 07 2016

Example

a(2)=6: 100001, 100010, 100100, 101000, 110000, 200000.

Mathematica

Rest@ CoefficientList[Series[(x - x^10)/(1 - x) ((1 - x^10)/(1 - x))^#, {x, 0, 9 (# + 1)}], x] &@ 5 (* or *)
Function[w, Count[w, #] & /@ Range[Max@ w]]@ Map[Total@ IntegerDigits@ # &, Range[10^#, 10^(# + 1) - 1]] &@ 5 (* Michael De Vlieger, Dec 07 2016 *)

Prog

(PARI) b=vector(54, i, 0); for(n=100000, 999999, a=eval(Vec(Str(n))); b[sum(j=1, 6, a[j])]++); for(n=1, 54, print1(b[n], ", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 19 2006

Crossrefs

Cf. A071817 3-digit numbers, A090579 4-digit numbers, A090580 5-digit numbers.

Sequence in context: A008488 A023031 A341203 * A000389 A143980 A140228

Adjacent sequences: A090578 A090579 A090580 * A090582 A090583 A090584

Keyword

base,fini,full,nonn

Author

Hugo Pfoertner, Jan 12 2004

Status

approved