A074825 - OEIS

%I #11 Sep 08 2022 08:45:07

%S 5,4,2,-2,-10,-16,-4,46,142,250,262,4,-652,-1530,-1818,38,5662,14760,

%T 22028,15014,-22490,-95846,-172434,-154740,110500,733134,1556206,

%U 1875238,365334,-4306496,-11734244,-17112802,-9496002,25050298,90586134,157886356,142006676,-87803882

%N Binomial transform of reflected pentanacci numbers A074062: a(n) = Sum_{k=0..n} binomial(n,k)*A074062(k).

%H G. C. Greubel, <a href="/A074825/b074825.txt">Table of n, a(n) for n = 0..1000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-7,6,-3,2).

%F a(n) = 4*a(n-1) - 7*a(n-2) + 6*a(n-3) - 3*a(n-4) + 2*a(n-5), a(0)=5, a(1)=4, a(2)=2, a(3)=-2, a(4)=-10.

%F G.f.: (5 -16*x +21*x^2 -12*x^3 +3*x^4)/(1 -4*x +7*x^2 -6*x^3 +3*x^4 -2*x^5).

%t CoefficientList[Series[(5-16x+21x^2-12x^3+3x^4)/(1-4x+7x^2-6x^3+3x^4-2x^5), {x, 0, 40}], x]

%t LinearRecurrence[{4,-7,6,-3,2},{5,4,2,-2,-10},40] (* _Harvey P. Dale_, Nov 29 2019 *)

%o (Magma) I:=[5,4,2,-2,-10]; [n le 5 select I[n] else 4*Self(n-1) -7*Self(n-2) +6*Self(n-3) -3*Self(n-4) +2*Self(n-5): n in [1..51]]; // _G. C. Greubel_, Jul 05 2021

%o (Sage)

%o def A074825_list(prec):

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

%o     return P( (5-16*x+21*x^2-12*x^3+3*x^4)/(1-4*x+7*x^2-6*x^3+3*x^4-2*x^5) ).list()

%o A074825_list(50) # _G. C. Greubel_, Jul 05 2021

%Y Cf. A074062.

%K easy,sign

%O 0,1

%A Mario Catalani (mario.catalani(AT)unito.it), Sep 09 2002