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 A159582 #9 Jun 29 2017 12:05:19 %S A159582 1,6,7,34,41,198,239,1154,1393,6726,8119,39202,47321,228486,275807, %T A159582 1331714,1607521,7761798,9369319,45239074,54608393,263672646, %U A159582 318281039,1536796802,1855077841,8957108166,10812186007,52205852194,63018038201,304278004998 %N A159582 Expansion of (1+6*x+x^2-2*x^3)/((x^2+2*x-1)*(x^2-2*x-1)), bisection is NSW numbers. %C A159582 Define c = [0, 7, 0, 41, 0, 239, 0, 1393, 0, 8119, 0, 47321, ...] where (c(2n+1)) = A002315(n+1) (NSW numbers). Then (a(n)) has the property c(2n) - a(2n) = -a(2n) = -A002315(n) and c(2n+1) - a(2n+1) = A002315(n) (NSW numbers). %H A159582 Colin Barker, <a href="/A159582/b159582.txt">Table of n, a(n) for n = 0..1000</a> %H A159582 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,6,0,-1). %F A159582 a(n) = 3*A078057(n)/2 - (-1)^n*A078057(n)/2. - _R. J. Mathar_, Nov 10 2009 %F A159582 From _Colin Barker_, Jun 29 2017: (Start) %F A159582 a(n) = 6*a(n-2) - a(n-4) for n>3. %F A159582 a(n) = ((-(-2+sqrt(2))*(-1+sqrt(2))^n - (-1-sqrt(2))^n*(2+sqrt(2)) - 3*(-(1-sqrt(2))^n*(-2+sqrt(2)) - (1+sqrt(2))^n*(2+sqrt(2))))) / (4*sqrt(2)). %F A159582 (End) %o A159582 (PARI) Vec((1+6*x+x^2-2*x^3) / ((x^2+2*x-1)*(x^2-2*x-1)) + O(x^50)) \\ _Colin Barker_, Jun 29 2017 %Y A159582 Cf. A002315. %K A159582 easy,nonn %O A159582 0,2 %A A159582 _Creighton Dement_, Apr 16 2009