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

Author

Gary W. Adamson, Apr 29 2008

Keywords

• nonn
• easy

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

Examples

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

Links

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

Crossrefs

Cf. A139634, A139635.

Programs

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 *)

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)

Extensions

More terms from Emeric Deutsch, May 05 2008

More terms from Colin Barker, Oct 10 2013