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 A350668 #39 Dec 25 2024 02:02:01
%S A350668 2,4,6,11,13,15,20,22,24,29,31,33,38,40,42,47,49,51,56,58,60,65,67,69,
%T A350668 74,76,78,83,85,87,92,94,96,101,103,105,110,112,114,119,121,123,128,
%U A350668 130,132,137,139,141,146,148
%N A350668 Numbers congruent to 2, 4, and 6 modulo 9: positions of 2 in A159955.
%C A350668 This sequence, together with A350666 and A350667, gives a 3-set partition of the nonnegative integers.
%C A350668 This sequence {a(n)}_{n>=0} gives the indices of the row sequences of array A = A347834, that are modulo 6 periodic with period length 3, namely
%C A350668 {A347834(a(n), m) mod 6}_{m >= 0} = {repeat(3, 1, 5)}.
%H A350668 Harvey P. Dale, <a href="/A350668/b350668.txt">Table of n, a(n) for n = 0..1000</a>
%H A350668 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A350668 A159955(a(n)) = 2.
%F A350668 Trisection: a(3*k) = 2 + 9*k, a(3*k + 1) = 4 + 9*k, and a(3*k + 3) = 6 + 9*k, for k >= 0.
%F A350668 G.f.: (2 + 2*x + 2*x^2 + 3*x^3)/((1 - x)*(1 - x^3)).
%F A350668 a(n) = 1 + 3*n + cos(2*n*Pi/3) + sin(2*n*Pi/3)/sqrt(3). - _Stefano Spezia_, Jan 30 2022
%F A350668 a(n) = 1 + 3*n + S(2*n, 1) = 1+3*n+A057078(n), with the Chebyshev S polynomials from A049310, using the partial fraction decomposition of the g.f., or the previous formula.
%e A350668 Rows of array {A347834(a(n), m)}_{m >= 0}, with modulo 6 congruence:
%e A350668 n = 0: row 2: {3, 13, 53, 213, 853, 3413, 13653, ...} mod 6 = {repeat(3, 1, 5)},
%e A350668 n = 1: row 4: {9, 37, 149, 597, 2389, 9557, ...} (mod 6) = {repeat(3, 1, 5)},
%e A350668 ...
%t A350668 Select[Range[0, 150], MemberQ[{2, 4, 6}, Mod[#, 9]] &] (* _Amiram Eldar_, Jan 29 2022 *)
%t A350668 LinearRecurrence[{1,0,1,-1},{2,4,6,11},80] (* _Harvey P. Dale_, Jul 12 2024 *)
%Y A350668 Cf. A049310, A159955, A347834, A350666, A350667.
%K A350668 nonn,easy
%O A350668 0,1
%A A350668 _Wolfdieter Lang_, Jan 29 2022