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 A092809 #12 Sep 09 2016 14:26:35 %S A092809 1,1,4,5,16,21,64,85,256,341,1024,1365,4096,5461,16384,21845,65536, %T A092809 87381,262144,349525,1048576,1398101,4194304,5592405,16777216, %U A092809 22369621,67108864,89478485,268435456,357913941,1073741824,1431655765,4294967296,5726623061 %N A092809 Expansion of (1+x-x^2) / ((1-x^2)*(1-4*x^2)). %C A092809 Partial sums of A092808. %C A092809 Apply matrix A133080 to A001045(n+1). - _Paul Barry_, Oct 08 2009 %H A092809 Colin Barker, <a href="/A092809/b092809.txt">Table of n, a(n) for n = 0..1000</a> %H A092809 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,0,-4) %F A092809 a(n) = 5*2^n/6+(-2)^n/6+(-1)^n/6-1/6. %F A092809 a(2*n) = 4^n = A000302(n). %F A092809 a(2*n+1) = (4*4^n-1)/3 = A002450(n+1). %F A092809 From _Colin Barker_, Sep 09 2016: (Start) %F A092809 a(n) = 5*a(n-2)-4*a(n-4) for n>3. %F A092809 G.f.: (1+x-x^2) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)) %F A092809 (End) %o A092809 (PARI) Vec((1+x-x^2)/((1-x)*(1+x)*(1-2*x)*(1+2*x)) + O(x^40)) \\ _Colin Barker_, Sep 09 2016 %o A092809 (PARI) a(n) = if(n%2,2,3)<<n \ 3 \\ _Charles R Greathouse IV_, Sep 09 2016 %Y A092809 Cf. A001045. %K A092809 easy,nonn %O A092809 0,3 %A A092809 _Paul Barry_, Mar 10 2004