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

Author

Hugo Pfoertner, Jan 12 2004

Keywords

• base
• fini
• full
• nonn

Comments

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

Examples

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

Crossrefs

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

Programs

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 *)

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

Formula

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