%I #23 Feb 08 2022 20:18:17

%S 1,13,37,85,181,373,757,1525,3061,6133,12277,24565,49141,98293,196597,

%T 393205,786421,1572853,3145717,6291445,12582901,25165813,50331637,

%U 100663285,201326581,402653173,805306357,1610612725,3221225461,6442450933,12884901877

%N Binomial transform of [1, 12, 12, 12, ...].

%C 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

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).

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

%F a(n) = 12*2^(n-1) - 11. - _Emeric Deutsch_, May 05 2008

%F a(n) = 2*a(n-1) + 11 (with a(1)=1). - _Vincenzo Librandi_, Nov 24 2010

%F From _Colin Barker_, Oct 10 2013: (Start)

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

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

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

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

%p seq(12*2^(n-1)-11,n=1..25); # _Emeric Deutsch_, May 05 2008

%t 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 *)

%Y Cf. A139634, A139635.

%K nonn,easy

%O 1,2

%A _Gary W. Adamson_, Apr 29 2008

%E More terms from _Emeric Deutsch_, May 05 2008

%E More terms from _Colin Barker_, Oct 10 2013