A331672 -id:A331672 - cp's OEIS frontend

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

J. M. Bergot, Jul 18 2007

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

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

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

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

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

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

A331673 Sum of all base-n numbers with digit sum n and length exactly n.

Original entry on oeis.org

3, 79, 2299, 84361, 3872406, 216591677, 14378073683, 1107635176621, 97229999995138, 9583904327477305, 1048274845801847390, 126003010469828661807, 16510208629407273871884, 2342241434486480710216185, 357676630651821282153992579, 58498575553741083746904253333

Offset: 2

Alois P. Heinz, Feb 22 2020

The cardinality of these numbers is given by A030662(n-1)

			a(2) = 3 = 11_2.
a(3) = 79 = 11 + 13 + 15 + 19 + 21 = 102_3 + 111_3 + 120_3 + 201_3 + 210_3.

Alois P. Heinz, Table of n, a(n) for n = 2..200

Cf. A007953, A030662, A130835, A331672.

b:= proc(n, i, k) option remember; `if`(n=0, [1, 0],
      `if`(i=0, 0, add((p->[p[1], p[2]*k+p[1]*d])(
         b(n-d, i-1, k)), d=0..min(n, k-1))))
    end:
a:= n-> b(n$3)[2]-b(n, n-1, n)[2]:
seq(a(n), n=2..17);

cp's OEIS Frontend

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

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