%I #12 Jun 30 2023 15:26:47
%S 221,1938,8673,73729,589855,7561526,34593784,218391421,2116566392,
%T 8522858480,34225586144,137170649024,549219204992,2197950037760,
%U 8793946586624,35180079217664,140728902612992,562932781936640
%N a(n) = 6*a(n-1)-8*a(n-2) for n > 10; a(0)=221, a(1)=1938, a(2)=8673, a(3)=73729, a(4)=589855, a(5)=7561526, a(6)=34593784, a(7)=218391421, a(8)=2116566392, a(9)=8522858480, a(10)=34225586144.
%C Related to Reverse and Add trajectory of 442 in base 2: a(n) = A075268(4*n+2)/6, i.e., one sixth of third quadrisection of A075268.
%H Vincenzo Librandi, <a href="/A177422/b177422.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) = 2*4^(n+7)-4192257*2^(n-5) for n > 8.
%F G.f.: (221+612*x-1187*x^2+37195*x^3+216865*x^4+4612228*x^5-6056532*x^6 +71320925*x^7+1082968138*x^8-2429408504*x^9+20966400*x^10) / ((1-2*x)*(1-4*x)).
%F G.f. for the sequence starting at a(9): 16*x^9*(532678655-1056972796*x)/((1-2*x)*(1-4*x)).
%t CoefficientList[Series[(221 + 612 x - 1187 x^2 + 37195 x^3 + 216865 x^4 + 4612228 x^5 - 6056532 x^6 + 71320925 x^7 + 1082968138 x^8 - 2429408504 x^9 + 20966400 x^10)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)
%o (PARI) {m=18; v=concat([221, 1938, 8673, 73729, 589855, 7561526, 34593784, 218391421, 2116566392, 8522858480, 34225586144], vector(m-11)); for(n=12, m, v[n]=6*v[n-1]-8*v[n-2]); v}
%o (Magma) [221, 1938, 8673, 73729, 589855, 7561526, 34593784, 218391421, 2116566392] cat [2*4^(n+7)-4192257*2^(n-5): n in [9..25]]; // _Vincenzo Librandi_, Sep 24 2013
%Y Cf. A075268 (Reverse and Add trajectory of 442 in base 2), A177420, A177421, A177423.
%K nonn,easy
%O 0,1
%A _Klaus Brockhaus_, May 07 2010