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A380976 a(0) = 0, a(1) = 1. Thereafter, a(n) = a(n-1) + a(n-2) converted to base n, read in base n+1.

%I A380976 #42 Feb 15 2025 02:13:10
%S A380976 0,1,1,2,3,6,10,18,31,54,93,172,300,536,955,1686,2976,5224,9491,17089,
%T A380976 30618,54774,97553,172749,305164,554749,982005,1757750,3140769,
%U A380976 5584153,9924579,17582197,31100841,56191241,99509416,177595495,316647651,564436376,1002970166
%N A380976 a(0) = 0, a(1) = 1. Thereafter, a(n) = a(n-1) + a(n-2) converted to base n, read in base n+1.
%H A380976 Alois P. Heinz, <a href="/A380976/b380976.txt">Table of n, a(n) for n = 0..4302</a>
%e A380976 a(5) = a(4) + a(3) = 5 = 10_5 -> 10_6 = 6.
%e A380976 a(13) = a(12) + a(11) = 472 = 2A4_13 -> 2A4_14 = 536.
%p A380976 a:= proc(n) option remember; `if`(n<2, n, (l-> add(l[i]*
%p A380976      (n+1)^(i-1), i=1..nops(l)))(convert(a(n-1)+a(n-2), base, n)))
%p A380976     end:
%p A380976 seq(a(n), n=0..43);  # _Alois P. Heinz_, Feb 12 2025
%t A380976 A380976[n_] := A380976[n] = If[n <= 1, n, FromDigits[IntegerDigits[A380976[n-1] + A380976[n-2], n], n+1]];
%t A380976 Array[A380976, 50, 0] (* _Paolo Xausa_, Feb 14 2025 *)
%o A380976 (Python)
%o A380976 from itertools import count, islice
%o A380976 from sympy.ntheory.digits import digits
%o A380976 def fromdigits(digs, base): return sum(d*base**i for i, d in enumerate(digs[::-1]))
%o A380976 def agen(): # generator of terms
%o A380976     yield from (a := [0, 1])
%o A380976     for n in count(2):
%o A380976         yield (an := fromdigits(digits(a[-2] + a[-1], n)[1:], n+1))
%o A380976         a = [a[-1], an]
%o A380976 print(list(islice(agen(), 37))) # _Michael S. Branicky_, Feb 11 2025
%K A380976 nonn,base
%O A380976 0,4
%A A380976 _Kaleb Williams_, Feb 10 2025