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

%I A332690 #21 Feb 21 2020 17:02:08
%S A332690 0,1,12,124,1248,12496,124992,1249984,12499968,124999936,1249999862,
%T A332690 12499999623,124999998144,1249999984364,12499999840480,
%U A332690 124999998308464,1249999981991936,12499999808733888,124999997974967808,1249999978624935680,12499999774999871588
%N A332690 Sum of all numbers in bijective base-9 numeration with digit sum n.
%C A332690 Different from A016134.
%H A332690 Alois P. Heinz, <a href="/A332690/b332690.txt">Table of n, a(n) for n = 0..1000</a>
%H A332690 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bijective_numeration">Bijective numeration</a>
%H A332690 <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 A332690 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 A332690 a(n) = A028904(A332691(n)).
%F A332690 a(n) = A016134(n-1) for n = 1..9.
%e A332690 a(2) = 12 = 2 + 10 = 2_bij9 + 11_bij9.
%p A332690 b:= proc(n) option remember; `if`(n=0, [1, 0], add((p->
%p A332690       [p[1], p[2]*9+p[1]*d])(b(n-d)), d=1..min(n, 9)))
%p A332690     end:
%p A332690 a:= n-> b(n)[2]:
%p A332690 seq(a(n), n=0..23);
%Y A332690 Cf. A007953, A016134, A028904, A052382, A211072, A214676, A332691.
%K A332690 nonn,base,easy
%O A332690 0,3
%A A332690 _Alois P. Heinz_, Feb 19 2020