A090579 Number of numbers with 4 decimal digits and sum of digits = n.

1, 4, 10, 20, 35, 56, 84, 120, 165, 219, 279, 342, 405, 465, 519, 564, 597, 615, 615, 597, 564, 519, 465, 405, 342, 279, 219, 165, 120, 84, 56, 35, 20, 10, 4, 1

Offset

1,2

Comments

There are 9000 numbers with 4 decimal digits, the smallest being 1000 and the largest 9999.

Links

Table of n, a(n) for n=1..36.

Formula

G.f.: (x-x^10)/(1-x)*((1-x^10)/(1-x))^3. - Geoffrey Critzer, Feb 09 2014

Example

a(2)=4: 1001, 1010, 1100, 2000.

Mathematica

nn=36; Drop[CoefficientList[Series[(x-x^10)/(1-x)(1-x^10)^3/(1-x)^3, {x, 0, nn}], x], 1] (* Geoffrey Critzer, Feb 09 2014 *)

Prog

(PARI) b=vector(36, i, 0); for(n=1000, 9999, a=eval(Vec(Str(n))); b[sum(j=1, 4, a[j])]++); for(n=1, 36, print1(b[n], ", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 19 2006

Crossrefs

Cf. A071817 3-digit numbers, A090580 5-digit numbers, A090581 6-digit numbers.

Sequence in context: A201722 A352208 A341193 * A276643 A000292 A352669

Adjacent sequences: A090576 A090577 A090578 * A090580 A090581 A090582

Keyword

base,fini,full,nonn

Author

Hugo Pfoertner, Jan 12 2004

Status

approved