A319969 -id:A319969 - cp's OEIS frontend

A322411 Compound tribonacci sequence with a(n) = A278040(A278041(n)), for n >= 0.

12, 36, 56, 80, 93, 117, 137, 161, 185, 205, 229, 242, 266, 286, 310, 330, 354, 367, 391, 411, 435, 459, 479, 503, 516, 540, 560, 584, 597, 621, 641, 665, 689, 709, 733, 746, 770, 790, 814, 834, 858, 871, 895, 915, 939, 963, 983, 1007, 1020, 1044, 1064, 1088, 1112, 1132, 1156, 1169, 1193, 1213, 1237, 1257, 1281

Offset: 0

Wolfdieter Lang, Jan 02 2019

The nine sequences A308199, A319967, A319968, A322410, A322409, A322411, A322413, A322412, A322414 are based on defining the tribonacci ternary word to start with index 0 (in contrast to the usual definition, in A080843 and A092782, which starts with index 1). As a result these nine sequences differ from the compound tribonacci sequences defined in A278040, A278041, and A319966-A319972. - N. J. A. Sloane, Apr 05 2019

L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Fibonacci representations of higher order, Fib. Quart., 10 (1972), 43-69.

Cf. A278040, A278041, A322410.

a(n) = A(C(n)) = A(C(n) + 1) - 2 = 4*A(n) + 3*B(n) + 2*n + 8, for n >= 0, with A = A278040 and C = A278041. For a proof see the W. Lang link in A278040, Proposition 9, eq. (50).
This formula already follows from Theorem 15 in the 1972 paper by Carlitz et al., which gives that b(c(n)) = a(n) + 2b(n) + 2c(n), where a, b and c are the classical positional sequences of the letters in the tribonacci word. The connection is made by using that c(n) = a(n) + b(n) + n, and by making the translation B(n) = a(n+1)-1, A(n) = b(n+1)-1, C(n) = c(n+1)-1. (Note the switching of A and B!). - Michel Dekking, Apr 07 2019
a(n+1) = A319969(n)-1 = A003145(A003146(n))-1, the corresponding classical compound tribonacci sequence. - Michel Dekking, Apr 04 2019

A319971 a(n) = A003146(A003145(n)).

Original entry on oeis.org

11, 35, 55, 79, 92, 116, 136, 160, 184, 204, 228, 241, 265, 285, 309, 329, 353, 366, 390, 410, 434, 458, 478, 502, 515, 539, 559, 583, 596, 620, 640, 664, 688, 708, 732, 745, 769, 789, 813, 833, 857, 870, 894, 914, 938, 962, 982, 1006, 1019, 1043, 1063, 1087

Offset: 1

N. J. A. Sloane, Oct 05 2018

nonn

By analogy with the Wythoff compound sequences A003622 etc., the nine compounds of A003144, A003145, A003146 might be called the tribonacci compound sequences. They are A278040, A278041, and A319966-A319972.

This sequence gives the positions of the word cabab in the tribonacci word t = abacabaa..., fixed point of the morphism a->ab, b->ac, c->a. This follows from the fact that the word bab is always preceded in t by the word ca, and the formula CB = BC-2, where A := A003144, B := A003145, C := A003146. See A319969 for BC, the positional sequence of the word bab. - Michel Dekking, Apr 09 2019

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Elena Barcucci, Luc Belanger and Srecko Brlek, On tribonacci sequences, Fib. Q., 42 (2004), 314-320. Compare page 318.
L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Fibonacci representations of higher order, Fib. Quart., 10 (1972), 43-69, Theorem 13.

Cf. A003144, A003145, A003146, A003622, A278039, A278040, A278041, and A319966-A319972.

a(n) = A003146(A003145(n)).

a(n) = 3*A003144(n) + 4*A003145(n) + 2*(n-1) = 4*A278040(n-1) + 3*A278039(A27n-1) + 2*n + 5, n >= 1. For a proof see the W. Lang link in A278040, Proposition 9, eq. (54). Wolfdieter Lang, Apr 11 2019

More terms from Rémy Sigrist, Oct 16 2018

cp's OEIS Frontend

A322411 Compound tribonacci sequence with a(n) = A278040(A278041(n)), for n >= 0.

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