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A176961 a(n) = (3*2^(n+1) - 8 - (-2)^n)/6.

%I A176961 #22 Sep 08 2022 08:45:53
%S A176961 1,2,8,12,36,52,148,212,596,852,2388,3412,9556,13652,38228,54612,
%T A176961 152916,218452,611668,873812,2446676,3495252,9786708,13981012,
%U A176961 39146836,55924052,156587348,223696212,626349396,894784852
%N A176961 a(n) = (3*2^(n+1) - 8 - (-2)^n)/6.
%H A176961 Vincenzo Librandi, <a href="/A176961/b176961.txt">Table of n, a(n) for n = 1..1000</a>
%H A176961 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-4).
%F A176961 a(n) - a(n-1) = A081631(n-2).
%F A176961 a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3).
%F A176961 G.f.: x*(1 + x + 2*x^2) / ((x-1)*(2*x+1)*(2*x-1)). - _R. J. Mathar_, Apr 30 2010
%F A176961 a(n) = 2^n - A084247(n-1). - _Bruno Berselli_, Sep 15 2011
%t A176961 a[1] := 1;
%t A176961 a[n_] := a[n] = a[n - 1]/2 + Sqrt[(5 + 4*(-1)^(n - 1))]/2:
%t A176961 Table[2^(n - 1)*a[n], {n, 1, 30}]
%o A176961 (PARI) a(n)=(3<<(n+1)-(-2)^n)\/6-1 \\ _Charles R Greathouse IV_, Sep 14 2011
%o A176961 (Magma) [(3*2^(n+1)-8-(-2)^n)/6:n in [1..40]]; // _Vincenzo Librandi_, Sep 15 2011
%K A176961 nonn,easy
%O A176961 1,2
%A A176961 _Roger L. Bagula_, Apr 29 2010