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 A289262 #23 Nov 23 2024 05:44:28
%S A289262 1,3,5,9,18,36,71,138,268,522,1017,1980,3853,7498,14594,28406,55287,
%T A289262 107604,209429,407614,793344,1544090,3005269,5849172,11384281,
%U A289262 22157298,43124882,83934214,163361667,317951804,618831521,1204435526,2344200136,4562530890
%N A289262 Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-...); [ ]=floor, r=11/7.
%C A289262 Conjecture: the sequence is strictly increasing.
%H A289262 Colin Barker, <a href="/A289262/b289262.txt">Table of n, a(n) for n = 0..1000</a>
%H A289262 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,-1,2,-2).
%F A289262 G.f.: 1/(Sum_{k>=0} [(k+1)*r]*(-x)^k), where r = 11/7 and [ ] = floor.
%F A289262 G.f.: (1 + x)^2*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6) / (1 - 2*x + x^2 - 2*x^3 + x^4 - 2*x^5 + 2*x^6). - _Colin Barker_, Jul 14 2017
%t A289262 r = 11/7;
%t A289262 u = 1000; (* # initial terms from given series *)
%t A289262 v = 100; (* # coefficients in reciprocal series *)
%t A289262 CoefficientList[Series[1/Sum[Floor[r*(k + 1)] (-x)^k, {k, 0, u}], {x, 0, v}], x]
%t A289262 LinearRecurrence[{2,-1,2,-1,2,-2},{1,3,5,9,18,36,71,138,268},40] (* _Harvey P. Dale_, Jun 11 2024 *)
%o A289262 (PARI) Vec((1 + x)^2*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6) / (1 - 2*x + x^2 - 2*x^3 + x^4 - 2*x^5 + 2*x^6) + O(x^50)) \\ _Colin Barker_, Jul 20 2017
%Y A289262 Cf. A078140 (includes guide to related sequences), A289267.
%K A289262 nonn,easy
%O A289262 0,2
%A A289262 _Clark Kimberling_, Jul 14 2017