A332691 Bijective base-9 representation of the sum of all numbers in bijective base-9 numeration with digit sum n.

1, 13, 147, 1636, 18124, 199399, 2314581, 25461653, 281178597, 3192976395, 35233852789, 387573484456, 4374418444135, 48228613881184, 541525753635894, 5956784387951128, 66635738355523786, 743994232656361639, 8285146556418623572, 92246623188575957748

Offset: 1

Author

Alois P. Heinz, Feb 19 2020

Keywords

• nonn
• base

Examples

			a(2) = 13_bij9 = 12 = 2 + 10 = 2_bij9 + 11_bij9.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..955
• Wikipedia, Bijective numeration

Crossrefs

Cf. A007953, A016134, A052382, A211072, A214676, A332690.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, [1, 0], add((p->
      [p[1], p[2]*9+p[1]*d])(b(n-d)), d=1..min(n, 9)))
    end:
g:= proc(n) local d, l, m; m, l:= n, "";
      while m>0 do d:= irem(m, 9, 'm');
        if d=0 then d:=9; m:= m-1 fi; l:= d, l
      od; parse(cat(l))
    end:
a:= n-> g(b(n)[2]):
seq(a(n), n=1..23);

Formula

a(n) = A052382(A332690(n)).