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

Author

Alois P. Heinz, Feb 22 2020

Keywords

• nonn
• base

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A007953, A030662, A130835, A331672.

Programs

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);