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A332690
Sum of all numbers in bijective base-9 numeration with digit sum n.
2
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
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);
KEYWORD
nonn,base,easy
AUTHOR
Alois P. Heinz, Feb 19 2020
STATUS
approved