A332690 - OEIS

%I #21 Feb 21 2020 17:02:08

%S 0,1,12,124,1248,12496,124992,1249984,12499968,124999936,1249999862,

%T 12499999623,124999998144,1249999984364,12499999840480,

%U 124999998308464,1249999981991936,12499999808733888,124999997974967808,1249999978624935680,12499999774999871588

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

%C Different from A016134.

%H Alois P. Heinz, <a href="/A332690/b332690.txt">Table of n, a(n) for n = 0..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Bijective_numeration">Bijective numeration</a>

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (10,1,-8,-17,-26,-35,-44,-53,-62,-81,-72,-63,-54,-45,-36,-27,-18,-9).

%F 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.

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

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

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

%p b:= proc(n) option remember; `if`(n=0, [1, 0], add((p->

%p       [p[1], p[2]*9+p[1]*d])(b(n-d)), d=1..min(n, 9)))

%p     end:

%p a:= n-> b(n)[2]:

%p seq(a(n), n=0..23);

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

%K nonn,base,easy

%O 0,3

%A _Alois P. Heinz_, Feb 19 2020