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

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

Offset

2,1

Comments

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

Links

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

Example

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

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]-b(n, n-1, n)[2]:
seq(a(n), n=2..17);

Crossrefs

Cf. A007953, A030662, A130835, A331672.

Sequence in context: A236574 A367249 A062660 * A065399 A265592 A105065

Adjacent sequences: A331670 A331671 A331672 * A331674 A331675 A331676

Keyword

nonn,base

Author

Alois P. Heinz, Feb 22 2020

Status

approved