cp's OEIS Frontend

A177421 a(n) = 6*a(n-1)-8*a(n-2)-9 for n > 10; a(0)=629, a(1)=6585, a(2)=26259, a(3)=221931, a(4)=1917027, a(5)=18285939, a(6)=125792217, a(7)=703932681, a(8)=7131271077, a(9)=26172260445, a(10)=103884128445.

%I A177421 #10 Jul 03 2023 11:33:31
%S A177421 629,6585,26259,221931,1917027,18285939,125792217,703932681,
%T A177421 7131271077,26172260445,103884128445,413926687101,1652487095037,
%U A177421 6603509073405,26401157680125,105578873493501,422263979519997,1688952889171965
%N A177421 a(n) = 6*a(n-1)-8*a(n-2)-9 for n > 10; a(0)=629, a(1)=6585, a(2)=26259, a(3)=221931, a(4)=1917027, a(5)=18285939, a(6)=125792217, a(7)=703932681, a(8)=7131271077, a(9)=26172260445, a(10)=103884128445.
%C A177421 Related to Reverse and Add trajectory of 442 in base 2: a(n) = A075268(4*n+1), i.e. second quadrisection of A075268.
%H A177421 Vincenzo Librandi, <a href="/A177421/b177421.txt">Table of n, a(n) for n = 0..1000</a>
%H A177421 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7, -14, 8).
%F A177421 a(n) = 6*4^(n+7)+12576771*2^(n-4)-3 for n > 8.
%F A177421 G.f.: (629+2182*x-11030*x^2+125276*x^3+678456*x^4+7763712*x^5+22853574*x^6 +64054092*x^7+3818545836*x^8-14897917296*x^9+14884638960*x^10-3900734400*x^11) / ((1-x)*(1-2*x)*(1-4*x)).
%F A177421 G.f. for the sequence starting at a(9): 3*x^9*(8724086815-26440564890*x+17716478072*x^2) / ((1-x)*(1-2*x)*(1-4*x)).
%t A177421 CoefficientList[Series[(629 + 2182 x - 11030 x^2 + 125276 x^3 + 678456 x^4 + 7763712 x^5 + 22853574 x^6 + 64054092 x^7 + 3818545836 x^8 - 14897917296 x^9 + 14884638960 x^10 - 3900734400 x^11)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)
%o A177421 (PARI) {m=18; v=concat([629, 6585, 26259, 221931, 1917027, 18285939, 125792217, 703932681, 7131271077, 26172260445, 103884128445], vector(m-11)); for(n=12, m, v[n]=6*v[n-1]-8*v[n-2]-9); v}
%o A177421 (Magma) [629, 6585, 26259, 221931, 1917027, 18285939, 125792217, 703932681, 7131271077] cat [6*4^(n+7)+12576771*2^(n-4)-3: n in [9..25]]; // _Vincenzo Librandi_, Sep 24 2013
%Y A177421 Cf. A075268 (Reverse and Add trajectory of 442 in base 2), A177420, A177422, A177423.
%K A177421 nonn,easy
%O A177421 0,1
%A A177421 _Klaus Brockhaus_, May 07 2010