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A131064 Binomial transform of [1, 1, 5, 5, 5, ...].

%I A131064 #32 Sep 08 2022 08:45:30
%S A131064 1,2,8,24,60,136,292,608,1244,2520,5076,10192,20428,40904,81860,
%T A131064 163776,327612,655288,1310644,2621360,5242796,10485672,20971428,
%U A131064 41942944,83885980,167772056,335544212,671088528,1342177164,2684354440
%N A131064 Binomial transform of [1, 1, 5, 5, 5, ...].
%C A131064 Row sums of triangle A131063. - _Emeric Deutsch_, Jun 20 2007
%H A131064 Vincenzo Librandi, <a href="/A131064/b131064.txt">Table of n, a(n) for n = 0..1000</a>
%H A131064 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A131064 From _Emeric Deutsch_, Jun 20 2007: (Start)
%F A131064 a(n) = 5*2^n - 4*(n + 1).
%F A131064 G.f.: (1-2*x+5*x^2)/((1-2*x)*(1-x)^2). (End)
%F A131064 a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). - _Vincenzo Librandi_, Jul 05 2012
%F A131064 E.g.f.: 5*exp(2*x) - 4*(1+x)*exp(x). - _G. C. Greubel_, Mar 12 2020
%e A131064 a(3) = 24 = sum of row 4 terms of A131063: (1 + 11 + 11 + 1).
%e A131064 a(3) = 24 = (1, 3, 3, 1) dot (1, 1, 5, 5).
%p A131064 a := proc (n) options operator, arrow; 5*2^n-4*n-4 end proc: seq(a(n), n = 0 .. 30); # _Emeric Deutsch_, Jun 20 2007
%t A131064 CoefficientList[Series[(1-2x+5x^2)/((1-2x)(1-x)^2),{x,0,40}],x] (* _Vincenzo Librandi_, Jul 05 2012 *)
%t A131064 LinearRecurrence[{4,-5,2},{1,2,8},30] (* _Harvey P. Dale_, Dec 29 2014 *)
%o A131064 (Magma) I:=[1, 2, 8]; [n le 3 select I[n] else 4*Self(n-1)-5*Self(n-2) + 2*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Jul 05 2012
%o A131064 (GAP) Print(List([0..30],n->5*2^n-4*n-4)); # _Muniru A Asiru_, Feb 21 2019
%o A131064 (Sage) [5*2^n -4*(n+1) for n in (0..30)] # _G. C. Greubel_, Mar 12 2020
%Y A131064 Cf. A109128, A123203, A131060, A131061, A131063, A131065, A131066, A131067, A131068.
%K A131064 nonn,easy
%O A131064 0,2
%A A131064 _Gary W. Adamson_, Jun 13 2007
%E A131064 Corrected and extended by _Emeric Deutsch_, Jun 20 2007