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%I #9 Sep 08 2022 08:45:53
%S 221,2754,12456,77697,589869,5333271,48222198,218509695,3071851356,
%T 12683673552,51137150880,205353516864,823023894144,3295315229952,
%U 13187700226560,52763679519744,211080475305984,844373415677952
%N a(n) = 6*a(n-1)-8*a(n-2) for n > 10; a(0)=221, a(1)=2754, a(2)=12456, a(3)=77697, a(4)=589869, a(5)=5333271, a(6)=48222198, a(7)=218509695, a(8)=3071851356, a(9)=12683673552, a(10)=51137150880.
%C Related to Reverse and Add trajectory of 442 in base 2: a(n) = A075268(4*n)/2, i.e. one half of first quadrisection of A075268.
%H Vincenzo Librandi, <a href="/A177420/b177420.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 (6, -8).
%F a(n) = 3*4^(n+7)-12576771*2^(n-5) for n > 8.
%F G.f.: (221+1428*x-2300*x^2+24993*x^3+223335*x^4+2415633*x^5 +20941524*x^6-28157325*x^7+2146570770*x^8-3999357024*x^9-390079584*x^10) / ((1-2*x)*(1-4*x)).
%F G.f. for the sequence starting at a(9): 48*x^9*(264243199-520101884*x) / ((1-2*x)*(1-4*x)).
%t CoefficientList[Series[(221 + 1428 x - 2300 x^2 + 24993 x^3 + 223335 x^4 + 2415633 x^5 + 20941524 x^6 - 28157325 x^7 + 2146570770 x^8 - 3999357024 x^9 - 390079584 x^10)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)
%t LinearRecurrence[{6,-8},{221,2754,12456,77697,589869,5333271,48222198,218509695,3071851356,12683673552,51137150880},20] (* _Harvey P. Dale_, Nov 02 2020 *)
%o (PARI) {m=18; v=concat([221, 2754, 12456, 77697, 589869, 5333271, 48222198, 218509695, 3071851356, 12683673552, 51137150880], vector(m-11)); for(n=12, m, v[n]=6*v[n-1]-8*v[n-2]); v}
%o (Magma) [221, 2754, 12456, 77697, 589869, 5333271, 48222198, 218509695,3071851356] cat [3*4^(n+7)-12576771*2^(n-5): n in [9..25]]; // _Vincenzo Librandi_, Sep 24 2013
%Y Cf. A075268 (Reverse and Add trajectory of 442 in base 2), A177421, A177422, A177423.
%K nonn,easy
%O 0,1
%A _Klaus Brockhaus_, May 07 2010
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