A054146 - OEIS

%I #9 Sep 08 2022 08:45:00

%S 0,1,6,29,128,536,2168,8556,33152,126640,478304,1789840,6646272,

%T 24519680,89956224,328437184,1194102784,4325299456,15615510016,

%U 56209986816,201798074368,722731821056,2582790830080,9211619462144

%N a(n) = A054145(n)/2.

%H G. C. Greubel, <a href="/A054146/b054146.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-20,16,-4).

%F From _G. C. Greubel_, Aug 01 2019: (Start)

%F a(n) = ((n-2)*((2 + sqrt(2))^n + (2 - sqrt(2))^n) + sqrt(2)*((2 + sqrt(2))^n - (2 - sqrt(2))^n))/16.

%F G.f.: x*(1 - x)^2/(1 - 4*x + 2*x^2)^2. (End)

%t LinearRecurrence[{8,-20,16,-4}, {0,1,6,29}, 30] (* _G. C. Greubel_, Aug 01 2019 *)

%o (PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1-x)^2/(1-4*x+2*x^2)^2)) \\ _G. C. Greubel_, Aug 01 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( x*(1-x)^2/(1-4*x+2*x^2)^2 )); // _G. C. Greubel_, Aug 01 2019

%o (Sage) (x*(1-x)^2/(1-4*x+2*x^2)^2).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 01 2019

%o (GAP) a:=[0,1,6,29];; for n in [5..30] do a[n]:=8*a[n-1]-20*a[n-2] +16*a[n-3]-4*a[n-4]; od; a; # _G. C. Greubel_, Aug 01 2019

%Y Cf. A054144, A054145.

%K nonn

%O 0,3

%A _Clark Kimberling_, Mar 18 2000