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A090580 Number of numbers with 5 decimal digits and sum of digits = n. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..45.

FORMULA

G.f.: (x - x^10)/(1 - x)*((1 - x^10)/(1 - x))^4. - Michael De Vlieger, Dec 07 2016

EXAMPLE

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

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 *)

PROG

(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

CROSSREFS

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

Sequence in context: A008487 A000743 A138779 * A000332 A140227 A264925

Adjacent sequences:  A090577 A090578 A090579 * A090581 A090582 A090583

KEYWORD

base,fini,full,nonn

AUTHOR

Hugo Pfoertner, Jan 12 2004

STATUS

approved

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Last modified March 27 13:47 EDT 2017. Contains 284176 sequences.