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%I #17 Sep 08 2022 08:45:11
%S 1,4,15,56,212,816,3184,12544,49728,197888,789248,3151872,12596224,
%T 50360320,201388032,805437440,3221504000,12885491712,51540852736,
%U 206161051648,824639225856,3298546417664,13194163650560,52776608464896
%N a(n) = 3*2^(2*(n-1)) + 2^(n-2)*(n+1).
%C Binomial transform of A047926.
%H Vincenzo Librandi, <a href="/A087438/b087438.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-20,16).
%F G.f.: (1 - 4*x + 3*x^2)/((1-2*x)^2*(1-4*x)).
%F E.g.f.: (3*exp(4*x) + (1+2*x)*exp(2*x))/4.
%F a(n) = 8*a(n-1) - 20*a(n-2) + 16*a(n-3); a(0)=1, a(1)=4, a(2)=15. - _Harvey P. Dale_, May 20 2011
%t LinearRecurrence[{8,-20,16},{1,4,15},30] (* or *) CoefficientList[ Series[ (1-4x+3x^2)/((1-2x)^2(1-4x)),{x,0,30}],x] (* _Harvey P. Dale_, May 20 2011 *)
%o (Magma) [3*2^(2*(n-1))+2^(n-2)*(n+1): n in [0..25]]; // _Vincenzo Librandi_, May 21 2011
%K easy,nonn
%O 0,2
%A _Paul Barry_, Sep 03 2003
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