A090580 Number of numbers with 5 decimal digits and sum of digits = n.

1, 5, 15, 35, 70, 126, 210, 330, 495, 714, 992, 1330, 1725, 2170, 2654, 3162, 3675, 4170, 4620, 4998, 5283, 5460, 5520, 5460, 5283, 4998, 4620, 4170, 3675, 3162, 2654, 2170, 1725, 1330, 992, 714, 495, 330, 210, 126, 70, 35, 15, 5, 1

Offset: 1

Author

Hugo Pfoertner, Jan 12 2004

Keywords

• base
• fini
• full
• nonn

Comments

There are 90000 numbers with 5 decimal digits, the smallest being 10000 and the largest 99999.

Examples

			a(2)=5: 10001, 10010, 10100, 11000, 20000.
		

Crossrefs

Cf. A071817 3-digit numbers, A090579 4-digit numbers, A090581 6-digit numbers.

Programs

Mathematica

Rest@ CoefficientList[Series[(x - x^10)/(1 - x) ((1 - x^10)/(1 - x))^4, {x, 0, 45}], x] (* or *)
Function[w, Count[w, #] & /@ Range[Max@ w]]@ Map[Total@ IntegerDigits@ # &, Range[10^#, 10^(# + 1) - 1]] &@ 4 (* Michael De Vlieger, Dec 07 2016 *)
Tally[Total[IntegerDigits[#]]&/@Range[10000,99999]][[All,2]] (* Harvey P. Dale, Jul 08 2019 *)

PARI

b=vector(45,i,0);for(n=10000,99999,a=eval(Vec(Str(n)));b[sum(j=1,5,a[j])]++);for(n=1,45,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))^4. - Michael De Vlieger, Dec 07 2016