A159696 a(0)=8, a(n) = 2*a(n-1) + 2^(n-1) for n > 0.

8, 17, 36, 76, 160, 336, 704, 1472, 3072, 6400, 13312, 27648, 57344, 118784, 245760, 507904, 1048576, 2162688, 4456448, 9175040, 18874368, 38797312, 79691776, 163577856, 335544320, 687865856, 1409286144, 2885681152, 5905580032, 12079595520, 24696061952, 50465865728

Offset

0,1

Comments

Diagonal of triangles A062111, A152920.

Links

G. C. Greubel, Table of n, a(n) for n = 0..3300

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

Formula

a(n) = Sum_{k=0..n} (k+8)*binomial(n,k).

From R. J. Mathar, Apr 20 2009: (Start)

a(n) = (16+n)*2^(n-1).

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

G.f.: (8-15*x)/(1-2*x)^2. (End)

E.g.f.: (x+8)*exp(2*x). - G. C. Greubel, Jun 02 2018

From Amiram Eldar, Oct 14 2025: (Start)

Sum_{n>=0} 1/a(n) = 131072*log(2) - 4092426112/45045.

Sum_{n>=0} (-1)^n/a(n) = 478785176/9009 - 131072*log(3/2). (End)

Example

a(0)=8, a(1) = 2*8 + 1 = 17, a(2) = 2*17 + 2 = 36, a(3) = 2*36 + 4 = 76, a(4) = 2*76 + 8 = 160, ...

Mathematica

LinearRecurrence[{4, -4}, {8, 17}, 30] (* G. C. Greubel, Jun 02 2018 *)
(* Alternative: *)
Table[(16+n)*2^(n-1), {n, 0, 30}] (* G. C. Greubel, Jun 02 2018 *)

Prog

(PARI) for(n=0, 30, print1((16+n)*2^(n-1), ", ")) \\ G. C. Greubel, Jun 02 2018
(Magma) [(16+n)*2^(n-1): n in [0..30]]; // G. C. Greubel, Jun 02 2018

Crossrefs

Cf. A000079, A001787, A001792, A034007, A045623, A045891, A062111, A111297, A152920, A159694, A159695.

Sequence in context: A226601 A106648 A209376 * A049713 A297728 A188129

Adjacent sequences: A159693 A159694 A159695 * A159697 A159698 A159699

Keyword

easy,nonn,changed

Author

Philippe Deléham, Apr 20 2009

Extensions

More terms from R. J. Mathar, Apr 20 2009

Status

approved