A139697 Binomial transform of [1, 12, 12, 12, ...].

1, 13, 37, 85, 181, 373, 757, 1525, 3061, 6133, 12277, 24565, 49141, 98293, 196597, 393205, 786421, 1572853, 3145717, 6291445, 12582901, 25165813, 50331637, 100663285, 201326581, 402653173, 805306357, 1610612725, 3221225461, 6442450933, 12884901877

Offset

1,2

Comments

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

Table of n, a(n) for n=1..31.

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

Formula

A007318 * [1, 12, 12, 12, ...].

a(n) = 12*2^(n-1) - 11. - Emeric Deutsch, May 05 2008

a(n) = 2*a(n-1) + 11 (with a(1)=1). - Vincenzo Librandi, Nov 24 2010

From Colin Barker, Oct 10 2013: (Start)

a(n) = 3*2^(n+1) - 11.

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

G.f.: x*(10*x+1)/((x-1)*(2*x-1)). (End)

E.g.f.: 5 - 11*exp(x) + 6*exp(2*x). - Elmo R. Oliveira, Nov 03 2025

Example

a(4) = 85 = (1, 3, 3, 1) dot (1, 12, 12, 12) = (1 + 36 + 36 + 12).

Maple

seq(12*2^(n-1)-11, n=1..25); # Emeric Deutsch, May 05 2008

Mathematica

a=1; lst={a}; k=12; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 17 2008 *)

Crossrefs

Cf. A007318, A099003, A139634, A139635, A139697, A139698, A139700, A139701.

Sequence in context: A155267 A157837 A039367 * A124706 A145990 A089528

Adjacent sequences: A139694 A139695 A139696 * A139698 A139699 A139700

Keyword

nonn,easy

Author

Gary W. Adamson, Apr 29 2008

Extensions

More terms from Emeric Deutsch, May 05 2008

More terms from Colin Barker, Oct 10 2013

Status

approved