A130835 Sum of all numbers having n or fewer digits and having the sum of their digits equal to n.

1, 33, 1110, 38885, 1399986, 51333282, 1906666476, 71499999285, 2701111108410, 102631111100848, 3917722222183045, 150126888888738762, 5771538888888311735, 222499777777775552780, 8598259999999991401740, 332968856666666633369781, 12918171566666666537484951

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..626

Formula

a(n) = (10^n-1)/9 * [x^n] ((x^10-1)/(x-1))^n. - Alois P. Heinz, Feb 07 2012

a(n) = A000042(n) * A167403(n) = A002275(n) * A167403(n). - Alois P. Heinz, Aug 16 2018

Example

Take n = 3. The numbers to be summed are 111, 3, 30, 300, 210, 201, 120, 102, 21 and 12, which add to 1110.

Maple

A007953 := proc(n) add(i, i=convert(n, base, 10)) ; end: A130835 := proc(n) local a, i; a := 0 ; for i from 1 to 10^n-1 do if A007953(i) = n then a := a+i ; fi ; od ; RETURN(a) ; end: seq(A130835(n), n=1..4) ; # R. J. Mathar, Aug 01 2007
# second Maple program:
b:= proc(n, i) option remember; `if`(n=0, 1,
      `if`(i=0, 0, add(b(n-j, i-1), j=0..min(n, 9))))
    end:
a:= n-> b(n, n)*(10^n-1)/9:
seq(a(n), n=1..20); # Alois P. Heinz, Nov 02 2009

Crossrefs

Cf. A000042, A002275, A007953, A167403, A211072, A331672, A331673.

Sequence in context: A371760 A293693 A187539 * A262101 A077420 A158688

Adjacent sequences: A130832 A130833 A130834 * A130836 A130837 A130838

Keyword

base,nonn

Author

J. M. Bergot, Jul 18 2007

Extensions

a(4)-a(6) from R. J. Mathar, Aug 01 2007

a(7)-a(12) from Donovan Johnson, Jul 02 2009

More terms from Alois P. Heinz, Nov 02 2009

Status

approved