A159695 a(0)=7, a(n) = 2*a(n-1) + 2^(n-1) for n > 0.

7, 15, 32, 68, 144, 304, 640, 1344, 2816, 5888, 12288, 25600, 53248, 110592, 229376, 475136, 983040, 2031616, 4194304, 8650752, 17825792, 36700160, 75497472, 155189248, 318767104, 654311424, 1342177280, 2751463424, 5637144576

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+7)*binomial(n,k).

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

a(n) = (14+n)*2^(n-1).

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

G.f.: (7-13*x)/(1-2x)^2. (End)

E.g.f.: (x+7)*exp(2*x). - G. C. Greubel, Jun 02 2018

From Amiram Eldar, Jan 19 2021: (Start)

Sum_{n>=0} 1/a(n) = 32768*log(2) - 204619418/9009.

Sum_{n>=0} (-1)^n/a(n) = 598484902/45045 - 32768*log(3/2). (End)

Example

a(0)=7, a(1) = 2*7 + 1 = 15, a(2) = 2*15 + 2 = 32, a(3) = 2*32 + 4 = 68, a(4) = 2*68 + 8 = 144, ...

Mathematica

LinearRecurrence[{4, -4}, {7, 15}, 30] (* or *) Table[(14+n)*2^(n-1), {n, 0, 30}] (* G. C. Greubel, Jun 02 2018 *)
nxt[{n_, a_}]:={n+1, 2a+2^n}; NestList[nxt, {0, 7}, 30][[All, 2]] (* Harvey P. Dale, Jan 01 2023 *)

Prog

(PARI) for(n=0, 30, print1((14+n)*2^(n-1), ", ")) \\ G. C. Greubel, Jun 02 2018
(Magma) [(14+n)*2^(n-1): n in [0..30]]; // G. C. Greubel, Jun 02 2018

Crossrefs

Cf. A000079, A001787, A001792, A045623, A045891, A034007, A111297, A159694.

Sequence in context: A120094 A078485 A233297 * A014001 A291642 A271995

Adjacent sequences: A159692 A159693 A159694 * A159696 A159697 A159698

Keyword

easy,nonn

Author

Philippe Deléham, Apr 20 2009

Extensions

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

Status

approved