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 A122678 #18 Feb 06 2025 08:20:43 %S A122678 1,6,21,61,166,441,1161,3046,7981,20901,54726,143281,375121,982086, %T A122678 2571141,6731341,17622886,46137321,120789081,316229926,827900701, %U A122678 2167472181,5674515846,14856075361,38893710241,101825055366,266581455861,697919312221,1827176480806 %N A122678 Invariant number of polygons of n-circum-C_5 H_5 systems. %C A122678 Note that the index in Eq. (5) of the paper must be 2k-1, not 2k as published, to reproduce the numbers. - _R. J. Mathar_, Nov 23 2014 %H A122678 Colin Barker, <a href="/A122678/b122678.txt">Table of n, a(n) for n = 1..1000</a> %H A122678 J. Brunvoll, S. J. Cyvin and B. N. Cyvin, <a href="http://match.pmf.kg.ac.rs/content34.htm">Azulenoids</a>, MATCH, No. 34, 1996, 91-108. %H A122678 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,1). %F A122678 a(n) = 5*Fibonacci(2*k-1)-4 = A106729(k-1)-4. %F A122678 G.f.: -x*(1+x)^2 / ( (x-1)*(x^2-3*x+1) ). - _R. J. Mathar_, Nov 23 2014 %F A122678 From _Colin Barker_, Nov 03 2016: (Start) %F A122678 a(n) = 2^(-1-n)*(-2^(3+n)-(-5+sqrt(5))*(3+sqrt(5))^n+(3-sqrt(5))^n*(5+sqrt(5))). %F A122678 a(n) = 4*a(n-1)-4*a(n-2)+a(n-3) for n>3. (End) %o A122678 (PARI) Vec(-x*(1+x)^2/((x-1)*(x^2-3*x+1)) + O(x^40)) \\ _Colin Barker_, Nov 03 2016 %K A122678 nonn,easy %O A122678 1,2 %A A122678 _N. J. A. Sloane_, Sep 23 2006