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<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 4, -8).

Table[(5-(-1)^n-6n)2^(n-2), {n, 0, 30}] (* or *) LinearRecurrence[{2, 4, -8}, {1, 0, -8}, 30] (* Harvey P. Dale, Mar 25 2021 *)

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_Johannes W. Meijer (meijgia(AT)hotmail.com), _, Jul 28 2010

a(n)=(5-(-1)^n-6*n)*2^(n-2)

1, 0, -8, -24, -80, -192, -512, -1152, -2816, -6144, -14336, -30720, -69632, -147456, -327680, -688128, -1507328, -3145728, -6815744, -14155776, -30408704, -62914560, -134217728, -276824064, -587202560, -1207959552, -2550136832

0,3

This sequence belongs to a family of sequences with GF(x) = (1+(k+2)*x+(2*k-4)*x^2)/(1-2*x-(k+8)*x^2-(2*k)*x^3). Among the members of this family are several red king sequences, see A179597. For the sequence given above, which is not a red king sequence, k = -4.

GF(x) = (1-2*x-12*x^2)/(1-2*x-4*x^2+8*x^3)

a(n) = 2*a(n-1)+4*a(n-2)-8*a(n-3) with a(1)=1, a(2)=0 and a(3)=-8.

a(n) = (5-(-1)^n-6*n)*2^(n-2)

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Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 28 2010

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