|
%I #13 Sep 08 2022 08:44:49
%S 1,25,85,215,477,985,1949,3755,7113,13329,24805,45959,84917,156625,
%T 288573,531323,977873,1799273,3310133,6089111,11200525,20601961,
%U 37893981,69699051,128197785,235793825,433693893,797688967,1467180389
%N a(n) = T(n,n+4), T given by A027023.
%H G. C. Greubel, <a href="/A027026/b027026.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 G.f.: x^4*(1 +21*x -10*x^2 -2*x^3 -7*x^4 +5*x^5)/((1-x)^3*(1-x-x^2-x^3)). - _Ralf Stephan_, Feb 11 2004
%F a(n) = A000213(n+4) -2*n*(n+3), n>3. - _R. J. Mathar_, Jun 24 2020
%p seq(coeff(series(x^4*(1 +21*x -10*x^2 -2*x^3 -7*x^4 +5*x^5)/((1-x)^3*(1-x-x^2-x^3)), x, n+1), x, n), n = 4..40); # _G. C. Greubel_, Nov 04 2019
%t Drop[CoefficientList[Series[x^4*(1+21*x-10*x^2-2*x^3-7*x^4 +5*x^5)/((1-x)^3*(1-x-x^2-x^3)), {x,0,40}], x], 4] (* or *) LinearRecurrence[{4, -5, 2,-1,2,-1}, {1,25,85,215,477,985}, 40] (* _G. C. Greubel_, Nov 04 2019 *)
%o (PARI) my(x='x+O('x^40)); Vec(x^4*(1 +21*x -10*x^2 -2*x^3 -7*x^4 +5*x^5)/((1-x)^3*(1-x-x^2-x^3))) \\ _G. C. Greubel_, Nov 04 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x^4*(1 +21*x -10*x^2 -2*x^3 -7*x^4 +5*x^5)/((1-x)^3*(1-x-x^2-x^3)) )); // _G. C. Greubel_, Nov 04 2019
%o (Sage)
%o def A027026_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P(x^4*(1 +21*x -10*x^2 -2*x^3 -7*x^4 +5*x^5)/((1-x)^3*(1-x-x^2-x^3))).list()
%o a=A027026_list(50); a[4:] # _G. C. Greubel_, Nov 04 2019
%o (GAP) a:=[1,25,85,215,477,985];; 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 04 2019
%K nonn,easy
%O 4,2
%A _Clark Kimberling_
|
