A139635 Binomial transform of [1, 11, 11, 11, ...].

1, 12, 34, 78, 166, 342, 694, 1398, 2806, 5622, 11254, 22518, 45046, 90102, 180214, 360438, 720886, 1441782, 2883574, 5767158, 11534326, 23068662, 46137334, 92274678, 184549366, 369098742, 738197494, 1476394998, 2952790006, 5905580022, 11811160054

Offset

1,2

Comments

A007318 * [1, 11, 11, 11, ...].

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) = 11*2^(n-1) - 10. - Emeric Deutsch, May 03 2008

a(n) = 2*a(n-1) + 10, with n > 1, a(1)=1. - Vincenzo Librandi, Nov 24 2010]

From Colin Barker, Mar 11 2014: (Start)

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

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

Example

a(4) = 78 = (1, 3, 3, 1) dot (1, 11, 11, 11) = (1 + 33 + 33 + 11).

Maple

seq(11*2^(n-1)-10, n=1.. 25); # Emeric Deutsch, May 03 2008

Mathematica

a=1; lst={a}; k=11; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 17 2008 *)
CoefficientList[Series[(9 x + 1)/((x - 1) (2 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 13 2014 *)
LinearRecurrence[{3, -2}, {1, 12}, 40] (* Harvey P. Dale, Oct 26 2015 *)

Prog

(PARI) Vec(x*(9*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 11 2014

Crossrefs

Cf. A139634.

Sequence in context: A113748 A069125 A142245 * A124705 A296154 A126366

Adjacent sequences: A139632 A139633 A139634 * A139636 A139637 A139638

Keyword

nonn,easy

Author

Gary W. Adamson, Apr 29 2008

Extensions

More terms from Emeric Deutsch, May 03 2008

More terms from Colin Barker, Mar 11 2014

Status

approved