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

%I A331673 #32 Feb 22 2020 22:55:51
%S A331673 3,79,2299,84361,3872406,216591677,14378073683,1107635176621,
%T A331673 97229999995138,9583904327477305,1048274845801847390,
%U A331673 126003010469828661807,16510208629407273871884,2342241434486480710216185,357676630651821282153992579,58498575553741083746904253333
%N A331673 Sum of all base-n numbers with digit sum n and length exactly n.
%C A331673 The cardinality of these numbers is given by A030662(n-1)
%H A331673 Alois P. Heinz, <a href="/A331673/b331673.txt">Table of n, a(n) for n = 2..200</a>
%e A331673 a(2) = 3 = 11_2.
%e A331673 a(3) = 79 = 11 + 13 + 15 + 19 + 21 = 102_3 + 111_3 + 120_3 + 201_3 + 210_3.
%p A331673 b:= proc(n, i, k) option remember; `if`(n=0, [1, 0],
%p A331673       `if`(i=0, 0, add((p->[p[1], p[2]*k+p[1]*d])(
%p A331673          b(n-d, i-1, k)), d=0..min(n, k-1))))
%p A331673     end:
%p A331673 a:= n-> b(n$3)[2]-b(n, n-1, n)[2]:
%p A331673 seq(a(n), n=2..17);
%Y A331673 Cf. A007953, A030662, A130835, A331672.
%K A331673 nonn,base
%O A331673 2,1
%A A331673 _Alois P. Heinz_, Feb 22 2020