A098656 Expansion of x(1-4x)/((1-2x)(1-8x^2)).

0, 1, -2, 4, -24, 16, -224, 64, -1920, 256, -15872, 1024, -129024, 4096, -1040384, 16384, -8355840, 65536, -66977792, 262144, -536346624, 1048576, -4292870144, 4194304, -34351349760, 16777216, -274844352512, 67108864, -2198889037824, 268435456, -17591649173504, 1073741824

Offset: 0

Author

Paul Barry, Sep 19 2004

Keywords

• easy
• sign

Comments

Let A=[1,2,1;2,0,-2;1,-2,1] the 3 X 3 symmetric Krawtchouk matrix. Than a(n) is the 1,3 element of A^n.

References

• P. Feinsilver and J. Kocik, Krawtchouk matrices from classical and quantum walks, Contemporary Mathematics, 287 2001, pp. 83-96.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,8,-16).

Crossrefs

Cf. A098655, A098657.

Programs

Mathematica

CoefficientList[Series[x (1-4x)/((1-2x)(1-8x^2)),{x,0,40}],x] (* or *) LinearRecurrence[{2,8,-16},{0,1,-2},40] (* Harvey P. Dale, Jun 30 2011 *)

Formula

a(n)=2^(n-1)-2^(3(n-1)/2)(1+(-1)^n)/sqrt(2); a(n)=2a(n-1)+8a(n-2)-16a(n-3).

a(n) = (-2)^(n-1)*A094024(n-1). - R. J. Mathar, Mar 08 2021