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%I #27 Sep 08 2022 08:45:10
%S 1,11,85,683,5461,43691,349525,2796203,22369621,178956971,1431655765,
%T 11453246123,91625968981,733007751851,5864062014805,46912496118443,
%U 375299968947541,3002399751580331,24019198012642645,192153584101141163
%N A Jacobsthal number sequence.
%C A trisection of A024495. - _Paul Curtz_, Nov 18 2007
%H Vincenzo Librandi, <a href="/A082365/b082365.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 a(n) = (4*8^n -(-1)^n)/3.
%F a(n) = J(3*n+2) = A001045(3*n)/3.
%F a(n) = 4*A015565(n)+A015565(n+1).
%F From _Philippe Deléham_, Nov 19 2007: (Start)
%F a(0)=1, a(1)=11, a(n+1) = 7*a(n) + 8*a(n-1) for n>=1 .
%F G.f.: (1+4*x)/(1-7*x-8*x^2). (End)
%t f[n_] := (4*8^n - (-1)^n)/3; Array[f, 20, 0] (* _Robert G. Wilson v_, Aug 13 2011 *)
%t LinearRecurrence[{7,8},{1,11},20] (* _Harvey P. Dale_, May 06 2012 *)
%o (Magma) [4*8^n/3-(-1)^n/3: n in [0..30]]; // _Vincenzo Librandi_, Aug 13 2011
%o (PARI) vector(30, n, n--; (4*8^n -(-1)^n)/3) \\ _G. C. Greubel_, Sep 16 2018
%Y Cf. A015565, A082311.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Apr 09 2003
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