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%I #36 Apr 09 2024 05:43:31
%S 1,-6,30,-156,804,-4152,21432,-110640,571152,-2948448,15220704,
%T -78573504,405618240,-2093913984,10809365376,-55800945408,
%U 288059973888,-1487045568000,7676542115328,-39628441869312,204573020169216,-1056062731892736,5451689048586240
%N a(n) = -4*a(n-1) + 6*a(n-2) for n > 1 with a(0) = 1 and a(1) = -6.
%H Reinhard Zumkeller, <a href="/A152223/b152223.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 (-4,6).
%F G.f.: (1 - 2*x)/(1 + 4*x - 6*x^2).
%F a(n) = Sum_{k=0..n} A147703(n,k)*(-7)^k.
%F a(n) = (1/2)*((-2 - sqrt(10))^n + (-2 + sqrt(10))^n) + (1/5)*sqrt(10)*((-2 - sqrt(10))^n - (-2 + sqrt(10))^n). - _Bruno Berselli_, Jan 12 2012
%t LinearRecurrence[{-4, 6}, {1, -6}, 23] (* _Bruno Berselli_, Jan 12 2012 *)
%o (PARI) Vec((1-2*x)/(1+4*x-6*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Jan 12 2012
%o (Haskell)
%o a152223 n = a152223_list !! n
%o a152223_list = 1 : -6 : zipWith (-)
%o (map (* 6) $ a152223_list) (map (* 4) $ tail a152223_list)
%o -- _Reinhard Zumkeller_, Jan 12 2012
%Y Cf. A147703.
%K sign,easy
%O 0,2
%A _Philippe Deléham_, Nov 29 2008
%E a(17)-a(23) corrected by _Charles R Greathouse IV_, Jan 12 2012
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