A168054 Expansion of (1-8x^2-24x^3)/((1-2x)^2*(1+2x+4x^2)).

1, 2, -4, -24, -48, -160, -448, -896, -2304, -5632, -11264, -26624, -61440, -122880, -278528, -622592, -1245184, -2752512, -6029312, -12058624, -26214400, -56623104, -113246208, -243269632, -520093696, -1040187392, -2214592512

Offset: 0

Author

Paul Barry, Nov 17 2009

Keywords

• easy
• sign

Comments

Hankel transform of A168055.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,8,-16).

Crossrefs

Cf. A168053, A168055.

Programs

Magma

I:=[1,2,-4,-24]; [n le 4 select I[n] else 2*Self(n-1)+8*Self(n-3)-16*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jul 08 2016

Mathematica

LinearRecurrence[{2, 0, 8, -16}, {1, 2, -4, -24}, 100] (* G. C. Greubel, Jul 07 2016 *)
CoefficientList[Series[(1 - 8 x^2 - 24 x^3) / ((1 - 2 x)^2 (1 + 2 x + 4 x^2)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 08 2016 *)

Formula

a(n) = 2^n*A168053(n).

a(n) = 2*a(n-1) + 8*a(n-3) - 16*a(n-4) for n>3. - Vincenzo Librandi, Jul 08 2016