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A159696 a(0)=8, a(n) = 2*a(n-1) + 2^(n-1) for n > 0. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Diagonal of triangles A062111, A152920.

LINKS

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

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

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] (* or *) 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, A045623, A045891, A034007, A111297, A159694, A159695.

Sequence in context: A226601 A106648 A209376 * A049713 A297728 A188129

Adjacent sequences:  A159693 A159694 A159695 * A159697 A159698 A159699

KEYWORD

easy,nonn

AUTHOR

Philippe Deléham, Apr 20 2009

EXTENSIONS

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

STATUS

approved

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Last modified June 25 10:10 EDT 2019. Contains 324351 sequences. (Running on oeis4.)