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

0, 1, 4, 48, 320, 2816, 21504, 176128, 1392640, 11206656, 89391104, 716177408, 5725224960, 45818576896, 366481506304, 2932120485888, 23455890145280, 187651416129536, 1501194149167104, 12009621912813568, 96076700424601600, 768614702908440576, 6148913225221013504

Offset

0,3

Links

Table of n, a(n) for n=0..22.

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

Formula

a(n) = A091905(n+1)/32.

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

E.g.f.: (exp(8*x) - exp(-4*x))/12. - Amiram Eldar, Feb 20 2026

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 *)

Crossrefs

Cf. A001045, A091905.

Sequence in context: A129002 A291623 A144704 * A192831 A158681 A269180

Adjacent sequences: A091901 A091902 A091903 * A091905 A091906 A091907

Keyword

easy,nonn

Author

Paul Barry, Feb 10 2004

Status

approved