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A127221 a(n) = 2^n*pentanacci(n) or (2^n)*A023424(n-1).

%I A127221 #22 Sep 19 2024 21:57:15
%S A127221 2,12,56,240,992,3648,14464,57088,224768,883712,3471360,13651968,
%T A127221 53682176,211075072,829915136,3263102976,12830244864,50447253504,
%U A127221 198353354752,779904614400,3066503888896,12057176965120,47407572189184,186401664532480,732912043425792
%N A127221 a(n) = 2^n*pentanacci(n) or (2^n)*A023424(n-1).
%H A127221 G. C. Greubel, <a href="/A127221/b127221.txt">Table of n, a(n) for n = 1..1000</a>
%H A127221 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,8,16,32).
%F A127221 a(n) = Trace of matrix [({2,2,2,2,2},{2,0,0,0,0},{0,2,0,0,0},{0,0,2,0,0},{0,0,0,2,0})^n].
%F A127221 a(n) = 2^n * Trace of matrix [({1,1,1,1,1},{1,0,0,0,0},{0,1,0,0,0},{0,0,1,0,0},{0,0,0,1,0})^n].
%F A127221 G.f.: -2*x*(1 +4*x +12*x^2 +32*x^3 +80*x^4)/(-1 +2*x +4*x^2 +8*x^3 +16*x^4 +32*x^5). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009; corrected by _R. J. Mathar_, Sep 16 2009
%F A127221 a(n) = 2*a(n-1)+4*a(n-2)+8*a(n-3)+16*a(n-4)+32*a(n-5). - _Colin Barker_, Sep 02 2013
%t A127221 Table[Tr[MatrixPower[2*{{1, 1, 1, 1, 1}, {1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}, x]], {x, 1, 20}]
%t A127221 LinearRecurrence[{2, 4, 8, 16, 32}, {2, 12, 56, 240, 992}, 50] (* _G. C. Greubel_, Dec 19 2017 *)
%o A127221 (PARI) x='x+O('x^30); Vec(-2*x*(1 +4*x +12*x^2 +32*x^3 +80*x^4)/(-1 +2*x +4*x^2 +8*x^3 +16*x^4 +32*x^5)) \\ _G. C. Greubel_, Dec 19 2017
%o A127221 (Magma) I:=[2, 12, 56, 240, 992]; [n le 5 select I[n] else 2*Self(n-1) + 4*Self(n-2) + 8*Self(n-3) + 16*Self(n-4) + 32*Self(n-5): n in [1..30]]; // _G. C. Greubel_, Dec 19 2017
%Y A127221 Cf. A087131, A127210, A127211, A127212, A127213, A127214, A127216, A001648, A127220, A127222.
%Y A127221 Cf. A023424, A074048.
%K A127221 nonn,easy
%O A127221 1,1
%A A127221 _Artur Jasinski_, Jan 09 2007
%E A127221 Definition corrected by _R. J. Mathar_, Sep 17 2009
%E A127221 More terms from _Colin Barker_, Sep 02 2013