A132397 - OEIS

%I #18 Jun 05 2020 10:34:14

%S 2,10,86,682,5462,43690,349526,2796202,22369622,178956970,1431655766,

%T 11453246122,91625968982,733007751850,5864062014806,46912496118442,

%U 375299968947542,3002399751580330,24019198012642646,192153584101141162

%N Second trisection of A024494.

%H Colin Barker, <a href="/A132397/b132397.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,8).

%F O.g.f.: 2(2x-1)/((x+1)(8x-1)). a(n) = 2*A082311(n). - _R. J. Mathar_, Jan 13 2008

%F a(0)=2, a(1)=10, a(n) = 7*a(n-1)+8*a(n-2). - _Harvey P. Dale_, Oct 14 2015

%F From _Oboifeng Dira_, Jun 05 2020: (Start)

%F a(n) = A078008(3*n+2). Third trisection of A078008.

%F a(n) = Sum_{k=0..n} binomial(3*n+2,3*k+1).

%F (End)

%F a(n) = 2*((-1)^n + 2^(1+3*n)) / 3 for n>1. - _Colin Barker_, Jun 05 2020

%t CoefficientList[Series[2(2x-1)/((x+1)(8x-1)),{x,0,30}],x] (* or *) LinearRecurrence[{7,8},{2,10},30] (* _Harvey P. Dale_, Oct 14 2015 *)

%o (PARI) Vec(2*(1 - 2*x) / ((1 + x)*(1 - 8*x)) + O(x^20)) \\ _Colin Barker_, Jun 05 2020

%Y Cf. A082311, A132805, A078008.

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Nov 20 2007

%E More terms from _R. J. Mathar_, Jan 13 2008