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

0,3

Comments

Different from A016134.

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).

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.

Example

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

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);

Crossrefs

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

Sequence in context: A120918 A262573 A039680 * A016134 A045507 A288350

Adjacent sequences: A332687 A332688 A332689 * A332691 A332692 A332693

Keyword

nonn,base,easy

Author

Alois P. Heinz, Feb 19 2020

Status

approved