A027055 - OEIS

%I #17 Sep 08 2022 08:44:49

%S 1,18,59,146,319,652,1281,2456,4637,8670,16111,29822,55067,101528,

%T 187013,344276,633561,1165674,2144419,3944650,7255831,13346084,

%U 24547849,45151152,83046581,152747190,280946647,516742262,950438067

%N a(n) = T(n, n+4), T given by A027052.

%H G. C. Greubel, <a href="/A027055/b027055.txt">Table of n, a(n) for n = 4..1003</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2,-1,2,-1).

%F From _Colin Barker_, Feb 19 2016: (Start)

%F a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3) -a(n-4) +2*a(n-5) -a(n-6) for n>9.

%F G.f.: x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3)).

%F (End)

%F a(n) = A001590(n+5) -n*(5+n), n>=4. - _R. J. Mathar_, Jun 15 2020

%p seq(coeff(series(x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3)), x, n+1), x, n), n = 4..40); # _G. C. Greubel_, Nov 06 2019

%t LinearRecurrence[{4,-5,2,-1,2,-1}, {1,18,59,146,319,652}, 40] (* _G. C. Greubel_, Nov 06 2019 *)

%o (PARI) my(x='x+O('x^40)); Vec(x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3))) \\ _G. C. Greubel_, Nov 06 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3)) )); // _G. C. Greubel_, Nov 06 2019

%o (Sage)

%o def A027053_list(prec):

%o     P.<x> = PowerSeriesRing(ZZ, prec)

%o     return P(x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3))).list()

%o a=A027053_list(40); a[4:] # _G. C. Greubel_, Nov 06 2019

%o (GAP) a:=[1,18,59,146,319,652];; for n in [7..40] do a[n]:=4*a[n-1] -5*a[n-2]+2*a[n-3]-a[n-4]+2*a[n-5]-a[n-6]; od; a; # _G. C. Greubel_, Nov 06 2019

%K nonn,easy

%O 4,2

%A _Clark Kimberling_