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

Author

Gary W. Adamson, Apr 29 2008

Keywords

• nonn
• easy

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

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A007318.

Programs

Magma

[10*2^(n-1)-9: n in [1..50]]; // Vincenzo Librandi, Mar 30 2014

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 *)

PARI

a(n)=10*2^(n-1)-9 \\ Charles R Greathouse IV, Oct 07 2015

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)

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Dec 17 2008

Simpler definition from Jon E. Schoenfield, Jun 23 2010