A091095 Expansion of (1+4*x-24*x^2)/((1-4*x)(1+4*x)).

1, 4, -8, 64, -128, 1024, -2048, 16384, -32768, 262144, -524288, 4194304, -8388608, 67108864, -134217728, 1073741824, -2147483648, 17179869184, -34359738368, 274877906944, -549755813888, 4398046511104, -8796093022208, 70368744177664, -140737488355328, 1125899906842624

Offset

0,2

Comments

a(0) = 1, a(2n-1) = k^(2n-1), a(2n) = (2-k)k^(2n-1), k = 4.

G.f.: (1+k*x+(2-2*k)*k*x^2)/((1-k*x)*(1+k*x)), k = 4.

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (0,16).

Formula

a(n) = 4^n/4 + (-3)*(-4)^n/4 + 6*0^n/4.

From Amiram Eldar, Feb 15 2026: (Start)

Sum_{n>=0} 1/a(n) = 17/15.

Sum_{n>=0} (-1)^n/a(n) = 3/5. (End)

Mathematica

LinearRecurrence[{0, 16}, {1, 4, -8}, 30] (* Harvey P. Dale, Dec 14 2019 *)

Crossrefs

Sequence in context: A214590 A215713 A120777 * A075787 A086891 A117636

Adjacent sequences: A091092 A091093 A091094 * A091096 A091097 A091098

Keyword

easy,sign

Author

Paul Barry, Dec 19 2003

Status

approved