A332690 Sum of all numbers in bijective base-9 numeration with digit sum n.

0, 1, 12, 124, 1248, 12496, 124992, 1249984, 12499968, 124999936, 1249999862, 12499999623, 124999998144, 1249999984364, 12499999840480, 124999998308464, 1249999981991936, 12499999808733888, 124999997974967808, 1249999978624935680, 12499999774999871588

Offset: 0

Author

Alois P. Heinz, Feb 19 2020

Keywords

• nonn
• base
• easy

Comments

Different from A016134.

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Wikipedia, Bijective numeration
• Index entries for linear recurrences with constant coefficients, signature (10,1,-8,-17,-26,-35,-44,-53,-62,-81,-72,-63,-54,-45,-36,-27,-18,-9).

Crossrefs

Cf. A007953, A016134, A028904, A052382, A211072, A214676, A332691.

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:
a:= n-> b(n)[2]:
seq(a(n), n=0..23);

Formula

G.f.: (Sum_{j=1..9} j*x^j) / ((B(x) - 1) * (9*B(x) - 1)) with B(x) = Sum_{j=1..9} x^j.

a(n) = A028904(A332691(n)).

a(n) = A016134(n-1) for n = 1..9.