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%I #26 Sep 08 2022 08:45:10
%S 1,8,36,148,596,2388,9556,38228,152916,611668,2446676,9786708,
%T 39146836,156587348,626349396,2505397588,10021590356,40086361428,
%U 160345445716,641381782868,2565527131476,10262108525908,41048434103636
%N a(n) = (7*4^n - 4)/3.
%C Binomial transform of A082541.
%H Vincenzo Librandi, <a href="/A083597/b083597.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 (5,-4).
%F a(n) = (7*4^n-4)/3.
%F G.f.: (1+3*x)/((1-4*x)*(1-x)).
%F E.g.f.: (7*exp(4*x)-4*exp(x))/3.
%F a(n) = 4*a(n-1) + 4, n > 0. - _Gary Detlefs_, Jun 23 2010
%F a(0)=1, a(1)=8, a(n) = 5*a(n-1) - 4*a(n-2). - _Harvey P. Dale_, Jul 23 2011
%F a(n) = A020988(n) + A020989(n), n >= 0. - _Yosu Yurramendi_, Mar 03 2017
%t (7*4^Range[0,25]-4)/3 (* or *) LinearRecurrence[{5,-4},{1,8},26] (* _Harvey P. Dale_, Jul 23 2011 *)
%t CoefficientList[Series[(1 + 3 x)/((1 - 4 x) (1 - x)), {x, 0, 22}], x] (* _Michael De Vlieger_, Mar 03 2017 *)
%o (Magma) [(7*4^n-4)/3: n in [0..25]]; // _Vincenzo Librandi_, Jul 24 2011
%o (PARI) a(n)=(7*4^n-4)/3 \\ _Charles R Greathouse IV_, Oct 07 2015
%K easy,nonn
%O 0,2
%A _Paul Barry_, May 02 2003
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