A290912 - OEIS

%I #23 Sep 18 2022 16:17:40

%S 0,1,4,16,68,287,1208,5088,21432,90273,380236,1601584,6745996,

%T 28414655,119684720,504121280,2123397744,8943915201,37672461204,

%U 158679314512,668369521108,2815224014047,11857940853032,49946562182048,210378775263272,886131640451169

%N a(n) = (1/6)*A290911(n).

%H Clark Kimberling, <a href="/A290912/b290912.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 (4, 0, 4, -1)

%F G.f.: x/(1 - 4 x - 4 x^3 + x^4). [Corrected by _A.H.M. Smeets_, Sep 12 2018]

%F a(n) = 4*a(n-1) + 4*a(n-3) - a(n-4).

%F a(n) = (1/6)*A290911(n) for n >= 0.

%p seq(coeff(series(x/(x^4-4*x^3-4*x+1),x,n+1), x, n), n = 0 .. 30); # _Muniru A Asiru_, Sep 12 2018

%t z = 60; s = x/(1 - x)^2; p = 1 - 6 s^2;

%t Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A000027 *)

%t u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A290911 *)

%t u/6 (* A290912 *)

%t LinearRecurrence[{4,0,4,-1},{0,1,4,16},30] (* _Harvey P. Dale_, Sep 18 2022 *)

%o (PARI) x='x+O('x^33); concat(0, Vec(x/(1-4*x-4*x^3+x^4))) \\ _Altug Alkan_, Sep 12 2018

%o (GAP) a:=[0,1,4,16];; for n in [5..30] do a[n]:=4*a[n-1]+4*a[n-3]-a[n-4]; od; a; # _Muniru A Asiru_, Sep 12 2018

%o (Magma) I:=[0,1,4,16]; [n le 4 select I[n] else 4*Self(n-1)+4*Self(n-3)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Sep 13 2018

%Y Cf. A000027, A290890, A290911.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Aug 18 2017