A159697 a(0)=9, a(n) = 2*a(n-1) + 2^(n-1) for n > 0.

9, 19, 40, 84, 176, 368, 768, 1600, 3328, 6912, 14336, 29696, 61440, 126976, 262144, 540672, 1114112, 2293760, 4718592, 9699328, 19922944, 40894464, 83886080, 171966464, 352321536, 721420288, 1476395008, 3019898880

Offset: 0

Author

Philippe Deléham, Apr 20 2009

Keywords

• easy
• nonn

Comments

Diagonal of triangles A062111, A152920.

Examples

			a(0)=9, a(1) = 2*9 + 1 = 19, a(2) = 2*19 + 2 = 40, a(3) = 2*40 + 4 = 84, a(4) = 2*84 + 8 = 176, ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..3300
• Index entries for linear recurrences with constant coefficients, signature (4, -4).

Crossrefs

Cf. A000079, A001787, A001792, A045623, A045891, A034007, A111297, A159694, A159695, A159696.

Programs

Magma

I:=[9,19]; [n le 2 select I[n] else 4*Self(n-1) - 4*Self(n-2): n in [1..30]]; // G. C. Greubel, Jun 02 2018

Mathematica

RecurrenceTable[{a[0]==9,a[n]==2a[n-1]+2^(n-1)},a,{n,30}] (* or *) LinearRecurrence[{4,-4},{9,19},30] (* Harvey P. Dale, Mar 24 2013 *)

PARI

Vec((9-17*x)/(1-2*x)^2 + O(x^40)) \\ Michel Marcus, Sep 29 2015

Formula

a(n) = Sum_{k=0..n} (k+9)*binomial(n,k).

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

a(n) = (18+n)*2^(n-1).

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

G.f.: (9-17*x)/(1-2*x)^2. (End)

a(0)=9, a(1)=19, a(n) = 4*a(n-1) - 4*a(n-2). - Harvey P. Dale, Mar 24 2013

a(n) = 2*A079862(n-10). - Michel Marcus, Sep 29 2015

E.g.f.: (x+9)*exp(2*x). - G. C. Greubel, Jun 02 2018

Extensions

More terms from Vincenzo Librandi, Apr 30 2009