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 A218985 #10 Nov 13 2017 09:35:07 %S A218985 5,23,103,459,2043,9091,40451,179987,800851,3563379,15855219,70547635, %T A218985 313900979,1396699187,6214598707,27651793203,123036370227, %U A218985 547449067315,2435869009715,10838374173491,48225234713395,214577687200563,954761218229043,4248200247317299 %N A218985 Power ceiling sequence of 2+sqrt(6). %C A218985 See A214992 for a discussion of power ceiling sequence and the power ceiling function, p4(x) = limit of a(n,x)/x^n. The present sequence is a(n,r), where r = 2+sqrt(6), and the limit p4(r) = 5.2127890589687233047437696796862841514303439... %C A218985 See A218984 for the power floor function, p1(x). For comparison of p4 and p1, limit(p4(r)/p1(r)) = 2*(1+sqrt(6))/5 = 1.379795897113271239278913629882356556786378... %H A218985 Clark Kimberling, <a href="/A218985/b218985.txt">Table of n, a(n) for n = 0..250</a> %H A218985 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-2,-2). %F A218985 a(n) = [x*a(n-1)], where x=2+sqrt(6), a(0) = [x]. %F A218985 a(n) = 5*a(n-1) - 2*a(n-2) - 2*a(n-3). %F A218985 G.f.: (5 - 2*x - 2*x^2)/(1 - 5*x + 2*x^2 + 2*x^3). %F A218985 a(n) = (1/15)*(-3 + (39-16*sqrt(6))*(2-sqrt(6))^n + (2+sqrt(6))^n*(39+16*sqrt(6))). - _Colin Barker_, Nov 13 2017 %e A218985 a(0) = ceiling(r) = 5, where r = 2+sqrt(6). %e A218985 a(1) = ceiling(5*r) = 23; a(2) = ceiling(23*r) = 103. %t A218985 (See A218984.) %o A218985 (PARI) Vec((5 - 2*x - 2*x^2) / ((1 - x)*(1 - 4*x - 2*x^2)) + O(x^40)) \\ _Colin Barker_, Nov 13 2017 %Y A218985 Cf. A214992, A090017, A123347, A218984. %K A218985 nonn,easy %O A218985 0,1 %A A218985 _Clark Kimberling_, Nov 11 2012