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 A322411 #20 Jan 05 2025 19:51:41 %S A322411 12,36,56,80,93,117,137,161,185,205,229,242,266,286,310,330,354,367, %T A322411 391,411,435,459,479,503,516,540,560,584,597,621,641,665,689,709,733, %U A322411 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 %N A322411 Compound tribonacci sequence with a(n) = A278040(A278041(n)), for n >= 0. %C A322411 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 %H A322411 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. %F A322411 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). %F A322411 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 %F A322411 a(n+1) = A319969(n)-1 = A003145(A003146(n))-1, the corresponding classical compound tribonacci sequence. - _Michel Dekking_, Apr 04 2019 %Y A322411 Cf. A278040, A278041, A322410. %K A322411 nonn,easy %O A322411 0,1 %A A322411 _Wolfdieter Lang_, Jan 02 2019