This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A319969 #25 Jan 05 2025 19:51:41 %S A319969 13,37,57,81,94,118,138,162,186,206,230,243,267,287,311,331,355,368, %T A319969 392,412,436,460,480,504,517,541,561,585,598,622,642,666,690,710,734, %U A319969 747,771,791,815,835,859,872,896,916,940,964,984,1008,1021,1045,1065,1089 %N A319969 a(n) = A003145(A003146(n)). %C A319969 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. %C A319969 This sequence gives the positions of the word bab in the tribonacci word t = abacabaa..., fixed point of the morphism a->ab, b->ac, c->a. This follows from the fact that the positional sequences of baa, bab and bac give a splitting of the positional sequence of the word ba, and the three sets BA(N), BB(N) and BC(N), give a splitting of the set B(N), where A := A003144, B := A003145, C := A003146. Here N denotes the set of positive integers. - _Michel Dekking_, Apr 09 2019 %H A319969 Rémy Sigrist, <a href="/A319969/b319969.txt">Table of n, a(n) for n = 1..10000</a> %H A319969 Elena Barcucci, Luc Belanger and Srecko Brlek, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/42-4/quartbarcucci04_2004.pdf">On tribonacci sequences</a>, Fib. Q., 42 (2004), 314-320. Compare page 318. %H A319969 L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/10-1/carlitz3-a.pdf">Fibonacci representations of higher order</a>, Fib. Quart., 10 (1972), 43-69, Theorem 13. %H A319969 Wolfdieter Lang, <a href="https://arxiv.org/abs/1810.09787">The Tribonacci and ABC Representations of Numbers are Equivalent</a>, arXiv preprint arXiv:1810.09787 [math.NT], 2018. %F A319969 a(n) = A003145(A003146(n)). %F A319969 a(n) = 3*A003144(n) + 4*A003145(n) + 2*n = 4*A276040(n-1) + 3*A278039(n-1) + 2*n + 7, n >= 1. For a proof see the W. Lang link, Proposition 9, eq. (50). - _Wolfdieter Lang_, Apr 11 2019 %Y A319969 Cf. A003144, A003145, A003146, A003622, A278039, A278040, A278041, and A319966-A319972. %K A319969 nonn %O A319969 1,1 %A A319969 _N. J. A. Sloane_, Oct 05 2018 %E A319969 More terms from _Rémy Sigrist_, Oct 16 2018