A139634 a(n) = 10*2^(n-1) - 9.

1, 11, 31, 71, 151, 311, 631, 1271, 2551, 5111, 10231, 20471, 40951, 81911, 163831, 327671, 655351, 1310711, 2621431, 5242871, 10485751, 20971511, 41943031, 83886071, 167772151, 335544311, 671088631, 1342177271, 2684354551

Offset

1,2

Comments

Binomial transform of [1, 10, 10, 10,...].

A007318 * [1, 10, 10, 10,...].

The binomial transform of [1, c, c, c,...] has the terms a(n)=1-c+c*2^(n-1) if the offset 1 is chosen. The o.g.f. of the a(n) is x{1+(c-2)x}/{(2x-1)(x-1)}. This applies to A139634 with c=10, to A139635 with c=11, to A139697 with c=12, to A139698 with c=25 and to A099003, A139700, A139701 accordingly. - R. J. Mathar, May 11 2008

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

a(n) = 2*a(n-1) + 9, with n>1, a(1)=1. - Vincenzo Librandi, Nov 24 2010

From Colin Barker, Oct 10 2013: (Start)

a(n) = 3*a(n-1) - 2*a(n-2).

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

Example

a(4) = 71 = (1, 3, 3, 1) dot (1, 10, 10, 10) = (1 + 30 + 30 + 10).

Maple

A139634:=n->10*2^(n-1)-9; seq(A139634(n), n=1..30); # Wesley Ivan Hurt, Mar 26 2014

Mathematica

a=1; lst={a}; k=10; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 17 2008 *)
CoefficientList[Series[(8 x + 1)/((x - 1) (2 x - 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 30 2014 *)
LinearRecurrence[{3, -2}, {1, 11}, 30] (* Harvey P. Dale, Feb 19 2023 *)

Prog

(Magma) [10*2^(n-1)-9: n in [1..50]]; // Vincenzo Librandi, Mar 30 2014
(PARI) a(n)=10*2^(n-1)-9 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A007318.

Sequence in context: A352954 A040973 A141884 * A173803 A124704 A293659

Adjacent sequences: A139631 A139632 A139633 * A139635 A139636 A139637

Keyword

nonn,easy

Author

Gary W. Adamson, Apr 29 2008

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Dec 17 2008

Simpler definition from Jon E. Schoenfield, Jun 23 2010

Status

approved