

A322411


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


7



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
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OFFSET

0,1


COMMENTS

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 A319966A319972.  N. J. A. Sloane, Apr 05 2019


LINKS

Table of n, a(n) for n=0..60.
L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Fibonacci representations of higher order, Fib. Quart., 10 (1972), 4369.


FORMULA

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


CROSSREFS

Cf. A278040, A278041, A322410.
Sequence in context: A076515 A039317 A298942 * A063298 A055926 A073762
Adjacent sequences: A322408 A322409 A322410 * A322412 A322413 A322414


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Jan 02 2019


STATUS

approved



