# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a291337 Showing 1-1 of 1 %I A291337 #9 Jun 02 2023 21:52:10 %S A291337 1,3,10,34,115,387,1300,4366,14665,49263,165490,555934,1867555, %T A291337 6273687,21075220,70798066,237832225,798950763,2683918570,9016098634, %U A291337 30287816995,101745987387,341795711140,1148195728966,3857138603785,12957301471863,43527515777650 %N A291337 p-INVERT of (1,1,1,1,1,...), where p(S) = 1 - 2 S - 2 S^3. %H A291337 Clark Kimberling, Table of n, a(n) for n = 0..1000 %H A291337 Index entries for linear recurrences with constant coefficients, signature (5,-7,5). %F A291337 G.f.: (1 - 2*x + 2*x^2)/(1 - 5*x + 7*x^2 - 5*x^3). %F A291337 a(n) = 5*a(n-1) - 7*a(n-2) + 5*a(n-3) for n >= 4. %F A291337 a(n) = (1/2)*A291005(n). %t A291337 z = 60; s = 1 - 2 s - 2 s^3; %t A291337 Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A000012 *) %t A291337 u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A291005 *) %t A291337 u / 2 (* A291337 *) %o A291337 (Magma) R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-2*x+2*x^2)/(1-5*x+7*x^2-5*x^3) )); // _G. C. Greubel_, Jun 01 2023 %o A291337 (SageMath) %o A291337 def A291337_list(prec): %o A291337 P. = PowerSeriesRing(ZZ, prec) %o A291337 return P( (1-2*x+2*x^2)/(1-5*x+7*x^2-5*x^3) ).list() %o A291337 A291337_list(30) # _G. C. Greubel_, Jun 01 2023 %Y A291337 Cf. A000012, A289780, A291000, A291005. %K A291337 nonn,easy %O A291337 0,2 %A A291337 _Clark Kimberling_, Aug 23 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE