A360260 - OEIS

%I #10 Feb 02 2023 14:43:53

%S 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 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 23,22,19,20,18,17,25,24,27,28,26,21,22,24,23,12,13,15

%N 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 See A356895 for the corresponding k's.

%C See A360259 for the Fibonacci variant.

%H Rémy Sigrist, <a href="/A360260/b360260.txt">Table of n, a(n) for n = 0..10609</a>

%F a(A027084(n)) = n - 1.

%e The first terms, alongside the corresponding k's, are:

%e   n   a(n)  k

%e   --  ----  ---

%e    0     0  N/A

%e    1     1    1

%e    2     3    2

%e    3     2    2

%e    4     5    3

%e    5     6    3

%e    6     4    3

%e    7     3    3

%e    8     8    4

%e    9    10    4

%e   10     9    4

%e   11     6    4

%e   12     7    4

%e   13     5    4

%e   14     4    4

%e   15    12    5

%o (PARI) tribonacci(n) = ([0,1,0; 0,0,1; 1,1,1]^n)[2,1]

%o { 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 Cf. A000073, A027084, A356895, A360259.

%K nonn,look

%O 0,3

%A _Rémy Sigrist_, Jan 31 2023