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 A133730 #14 Sep 04 2024 15:29:34
%S A133730 1,0,-1,1,1,1,-1,3,1,5,-1,11,1,21,-1,43,1,85,-1,171,1,341,-1,683,1,
%T A133730 1365,-1,2731,1,5461,-1,10923,1,21845,-1,43691,1,87381,-1,174763,1,
%U A133730 349525,-1,699051,1,1398101,-1,2796203,1,5592405,-1,11184811,1,22369621,-1,44739243,1
%N A133730 Alternating sign sequence A033999 interleaved with Jacobsthal sequence A001045.
%H A133730 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,2).
%F A133730 From _R. J. Mathar_, Jan 09 2008 (Start):
%F A133730 a(2n) = (-1)^n. a(2n+1) = A001045(n).
%F A133730 O.g.f.: -(x-1)*(x^2-x-1)/[(2*x^2-1)*(1+x^2)].
%F A133730 a(n) = A133684(n+1)-A133684(n).
%F A133730 First differences: a(2n)-a(2n+1) = -2*A001045(n-2) for n>=3; a(2n+1)-a(2n) = 4*A001045(n-2) for n >=2. (End)
%t A133730 LinearRecurrence[{0,1,0,2},{1,0,-1,1},70] (* _Harvey P. Dale_, Sep 04 2024 *)
%Y A133730 Cf. A033999, A001045, A133684.
%K A133730 sign,easy
%O A133730 0,8
%A A133730 _Paul Curtz_, Jan 04 2008
%E A133730 Edited by _R. J. Mathar_, Jan 09 2008
%E A133730 Definition amended by _Georg Fischer_, Nov 02 2021