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A177685 a(n) = 6*a(n-1)-8*a(n-2) for n > 4; a(0)=603, a(1)=4731, a(2)=58834, a(3)=254204, a(4)=1032696.

%I A177685 #12 Jun 30 2023 15:31:23
%S A177685 603,4731,58834,254204,1032696,4162544,16713696,66981824,268181376,
%T A177685 1073233664,4293950976,17177836544,68715411456,274869776384,
%U A177685 1099495366656,4398013988864,17592120999936,70368614088704
%N A177685 a(n) = 6*a(n-1)-8*a(n-2) for n > 4; a(0)=603, a(1)=4731, a(2)=58834, a(3)=254204, a(4)=1032696.
%C A177685 Related to Reverse and Add trajectory of 537 in base 2: a(n) = A077076(4*n+3)/6, i.e., one sixth of fourth quadrisection of A077076.
%H A177685 Vincenzo Librandi, <a href="/A177685/b177685.txt">Table of n, a(n) for n = 0..1000</a>
%H A177685 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -8).
%F A177685 a(n) = 4^(n+6)-1985*2^(n-1) for n > 2.
%F A177685 G.f.: (603+1113*x+35272*x^2-60952*x^3-21856*x^4) / ((1-2*x)*(1-4*x)).
%F A177685 G.f. for the sequence starting at a(3): 4*x^3*(63551-123132*x) / ((1-2*x)*(1-4*x)).
%t A177685 CoefficientList[Series[(603 + 1113 x + 35272 x^2 - 60952 x^3 - 21856 x^4)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)
%t A177685 LinearRecurrence[{6,-8},{603,4731,58834,254204,1032696},20] (* _Harvey P. Dale_, May 26 2019 *)
%o A177685 (PARI) {m=18; v=concat([603, 4731, 58834, 254204, 1032696], vector(m-5)); for(n=6 ,m, v[n]=6*v[n-1]-8*v[n-2]); v}
%o A177685 (Magma) [603, 4731, 58834] cat [4^(n+6)-1985*2^(n-1): n in [3..25]]; // _Vincenzo Librandi_, Sep 24 2013
%Y A177685 Cf. A077076 (Reverse and Add trajectory of 537 in base 2), A177682, A177683, A177684.
%K A177685 nonn
%O A177685 0,1
%A A177685 _Klaus Brockhaus_, May 12 2010