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8th binomial transform of the periodic sequence (1,9,1,1,9,1...).
4

%I #18 Jul 23 2024 16:21:34

%S 1,17,209,2273,23201,228017,2186609,20620673,192174401,1775688017,

%T 16304021009,148995991073,1356782533601,12321773100017,

%U 111671069983409,1010465414433473,9132169221980801,82455386442384017,743959522093353809,6708663007623467873,60469158230094196001

%N 8th binomial transform of the periodic sequence (1,9,1,1,9,1...).

%H Vincenzo Librandi, <a href="/A081035/b081035.txt">Table of n, a(n) for n = 0..300</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-63).

%F a(n) = 9*a(n-1) + 8*7^(n-1).

%F a(n) = 5*9^n - 4*7^n.

%F G.f.: (1+x)/((1-7*x)*(1-9*x)). - _Vincenzo Librandi_, Aug 06 2013

%F a(0)=1, a(1)=17, a(n)=16*a(n-1)-63*a(n-2). - _Harvey P. Dale_, Oct 07 2014

%F E.g.f.: exp(7*x)*(5*exp(2*x) - 4). - _Stefano Spezia_, Jul 23 2024

%t CoefficientList[Series[(1 + x)/((1 - 7 x) (1 - 9 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 06 2013 *)

%t LinearRecurrence[{16,-63},{1,17},30] (* _Harvey P. Dale_, Oct 07 2014 *)

%o (Magma) [5*9^n-4*7^n: n in [0..25]]; // _Vincenzo Librandi_, Aug 06 2013

%o (PARI) a(n)=5*9^n-4*7^n \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A081034, A081036.

%K nonn,easy

%O 0,2

%A _Paul Barry_, Mar 03 2003