A138340 Expansion of (1-8x)/(1-4x+16x^2).

1, -4, -32, -64, 256, 2048, 4096, -16384, -131072, -262144, 1048576, 8388608, 16777216, -67108864, -536870912, -1073741824, 4294967296, 34359738368, 68719476736, -274877906944, -2199023255552, -4398046511104, 17592186044416

Offset: 0

Author

Paul Barry, Mar 15 2008

Keywords

• easy
• sign

Comments

abs(a(n)) = 2^A047267(n).

Links

• Index entries for linear recurrences with constant coefficients, signature (4, -16).

Programs

Mathematica

CoefficientList[Series[(1-8x)/(1-4x+16x^2),{x,0,30}],x] (* or *) LinearRecurrence[{4,-16},{1,-4},30] (* Harvey P. Dale, Sep 30 2014 *)

Formula

a(n) = 2*4^n(cos(Pi*(n+1)/3) - sqrt(3)*sin(Pi*(n+1))/3).

a(n) = 4^n*Sum_{k=0..n} A121314(n,k)*(-1)^k*3^(n-k). - Philippe Deléham, Nov 01 2008

a(n) = A128018(n)*2^n. - Philippe Deléham, Nov 14 2008

a(n) = 4*a(n-1) - 16*a(n-2); a(0)=1, a(1)=-4. - Harvey P. Dale, Sep 30 2014