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 A319971 #20 Jan 05 2025 19:51:41 %S A319971 11,35,55,79,92,116,136,160,184,204,228,241,265,285,309,329,353,366, %T A319971 390,410,434,458,478,502,515,539,559,583,596,620,640,664,688,708,732, %U A319971 745,769,789,813,833,857,870,894,914,938,962,982,1006,1019,1043,1063,1087 %N A319971 a(n) = A003146(A003145(n)). %C A319971 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 A319971 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 %H A319971 Rémy Sigrist, <a href="/A319971/b319971.txt">Table of n, a(n) for n = 1..10000</a> %H A319971 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 A319971 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. %F A319971 a(n) = A003146(A003145(n)). %F A319971 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 %Y A319971 Cf. A003144, A003145, A003146, A003622, A278039, A278040, A278041, and A319966-A319972. %K A319971 nonn %O A319971 1,1 %A A319971 _N. J. A. Sloane_, Oct 05 2018 %E A319971 More terms from _Rémy Sigrist_, Oct 16 2018