A172160 a(0)=1. a(n) = 2^(n-2)*(5-n), for n>0.

1, 2, 3, 4, 4, 0, -16, -64, -192, -512, -1280, -3072, -7168, -16384, -36864, -81920, -180224, -393216, -851968, -1835008, -3932160, -8388608, -17825792, -37748736, -79691776, -167772160, -352321536, -738197504, -1543503872, -3221225472, -6710886400

Offset

0,2

Comments

The inverse binomial transform is 1,1,0,0,-1,-1,-2,-2,-3,-3 = essentially A168050 or the negative of A004526.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n+1) - 2*a(n) = -A131577(n).

a(n) + A001787(n-1) = A000079(n+1).

a(n+5) = -A059165(n) = 4*A159964(n+1).

G.f.: (1 - 2*x - x^2)/(1-2*x)^2. - R. J. Mathar, Feb 11 2010

a(n) = 4*a(n-1) - 4*a(n-2), n>2.

E.g.f.: (1/4)*((5-2*x)*exp(2*x) - 1). - G. C. Greubel, Apr 21 2022

a(n) = 4^n*A045891(1-n) if n>1. - Michael Somos, Apr 22 2022

Example

G.f. = 1 + 2*x + 3*x^2 + 4*x^3 + 4*x^4 - 16*x^6 - 64*x^7 + ... - Michael Somos, Apr 22 2022

Mathematica

Table[2^(n-2)*(5-n) -(1/4)*Boole[n==0], {n, 0, 40}] (* G. C. Greubel, Apr 21 2022 *)

Prog

(SageMath) [2^(n-2)*(5-n) -(1/4)*bool(n==0) for n in (1..40)] # G. C. Greubel, Apr 21 2022

Crossrefs

Cf. A004526, A045891, A168050.

Cf. A000079, A001787, A059165, A159964, A131577.

Sequence in context: A111362 A134581 A099587 * A171170 A256913 A346617

Adjacent sequences: A172157 A172158 A172159 * A172161 A172162 A172163

Keyword

sign,easy

Author

Paul Curtz, Jan 27 2010

Extensions

Definition replaced with closed form by R. J. Mathar, Feb 11 2010

Status

approved