A091904 Expansion of x/((1+4x)(1-8x)).

0, 1, 4, 48, 320, 2816, 21504, 176128, 1392640, 11206656, 89391104, 716177408, 5725224960, 45818576896, 366481506304, 2932120485888, 23455890145280, 187651416129536, 1501194149167104, 12009621912813568, 96076700424601600

Offset: 0

Author

Paul Barry, Feb 10 2004

Keywords

• easy
• nonn

Comments

A091904(n)=A091905(n+1)/50.

Links

• Index entries for linear recurrences with constant coefficients, signature (4,32).

Programs

Mathematica

Join[{a=0,b=1},Table[c=4*b+32*a;a=b;b=c,{n,30}]] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2011 *)
CoefficientList[Series[x/((1+4x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[{4,32},{0,1},30] (* Harvey P. Dale, May 06 2014 *)

Formula

a(n)=8^n/12-(-4)^n/12

a(0)=0, a(1)=1, a(n)=4*a(n-1)+32*a(n-2). - Harvey P. Dale, May 06 2014

a(n)=4^(n-1)*A001045(n+1). - R. J. Mathar, Mar 08 2021