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A360260 a(0) = 0, and for any n > 0, let k > 0 be as small as possible and such that T(3) + ... + T(2+k) >= n (where T(m) denotes A000073(m), the m-th tribonacci number); a(n) = k + a(T(3) + ... + T(2+k) - n).

%I A360260 #10 Feb 02 2023 14:43:53
%S A360260 0,1,3,2,5,6,4,3,8,10,9,6,7,5,4,12,11,14,15,13,8,9,11,10,7,8,6,5,16,
%T A360260 17,15,14,19,21,20,17,18,10,11,13,12,15,16,14,9,10,12,11,8,9,7,6,21,
%U A360260 23,22,19,20,18,17,25,24,27,28,26,21,22,24,23,12,13,15
%N A360260 a(0) = 0, and for any n > 0, let k > 0 be as small as possible and such that T(3) + ... + T(2+k) >= n (where T(m) denotes A000073(m), the m-th tribonacci number); a(n) = k + a(T(3) + ... + T(2+k) - n).
%C A360260 See A356895 for the corresponding k's.
%C A360260 See A360259 for the Fibonacci variant.
%H A360260 Rémy Sigrist, <a href="/A360260/b360260.txt">Table of n, a(n) for n = 0..10609</a>
%F A360260 a(A027084(n)) = n - 1.
%e A360260 The first terms, alongside the corresponding k's, are:
%e A360260   n   a(n)  k
%e A360260   --  ----  ---
%e A360260    0     0  N/A
%e A360260    1     1    1
%e A360260    2     3    2
%e A360260    3     2    2
%e A360260    4     5    3
%e A360260    5     6    3
%e A360260    6     4    3
%e A360260    7     3    3
%e A360260    8     8    4
%e A360260    9    10    4
%e A360260   10     9    4
%e A360260   11     6    4
%e A360260   12     7    4
%e A360260   13     5    4
%e A360260   14     4    4
%e A360260   15    12    5
%o A360260 (PARI) tribonacci(n) = ([0,1,0; 0,0,1; 1,1,1]^n)[2,1]
%o A360260 { t = k = 0; print1 (0); for (n = 1, #a = vector(70), if (n > t, t += tribonacci(2+k++);); print1 (", "a[n] = k+if (t==n, 0, a[t-n]));); }
%Y A360260 Cf. A000073, A027084, A356895, A360259.
%K A360260 nonn,look
%O A360260 0,3
%A A360260 _Rémy Sigrist_, Jan 31 2023