A331672 Sum of all base-n numbers with digit sum n and length at most n.

3, 91, 2635, 94501, 4254936, 234572213, 15403880115, 1176838159861, 102631111100848, 10063085278250005, 1095923297151849530, 131253123286275198027, 17145216226230367266330, 2425892898650501790637545, 369599184391990522425455939, 60326656013944234430010524773

Offset

2,1

Comments

The cardinality of these numbers is given by A048775(n-1).

Links

Alois P. Heinz, Table of n, a(n) for n = 2..322

Formula

a(n) = A048775(n-1)*A023037(n) = (binomial(2*n-1,n)-n)*(n^n-1)/(n-1).

Example

a(2) = 3 = 11_2.
a(3) = 91 = 5 + 7 + 11 + 13 + 15 + 19 + 21 = 12_3 + 21_3 + 102_3 + 111_3 + 120_3 + 201_3 + 210_3.
a(10) = A130835(10) = 102631111100848.

Maple

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]:
seq(a(n), n=2..17);
# second Maple program:
a:= n-> (binomial(2*n-1, n)-n)*(n^n-1)/(n-1):
seq(a(n), n=2..17);

Crossrefs

Cf. A007953, A023037, A048775, A130835, A331673.

Sequence in context: A366219 A300419 A156754 * A213978 A318129 A119121

Adjacent sequences: A331669 A331670 A331671 * A331673 A331674 A331675

Keyword

nonn,base

Author

Alois P. Heinz, Feb 22 2020

Status

approved