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A176635 a(n) = 6*a(n-1)-8*a(n-2) for n > 1; a(0) = 57, a(1) = 242.

%I A176635 #15 Jun 21 2023 09:18:50
%S A176635 57,242,996,4040,16272,65312,261696,1047680,4192512,16773632,67101696,
%T A176635 268421120,1073713152,4294909952,17179754496,68719247360,274877448192,
%U A176635 1099510710272,4398044676096,17592182374400,70368736837632
%N A176635 a(n) = 6*a(n-1)-8*a(n-2) for n > 1; a(0) = 57, a(1) = 242.
%C A176635 Related to Reverse and Add trajectory of 77 in base 2: a(n) = A075253(4*n+3)/12, i.e., one twelfth of fourth quadrisection of A075253.
%C A176635 Second binomial transform of 57 followed by 128*A000079.
%C A176635 Third binomial transform of A176636.
%H A176635 Vincenzo Librandi, <a href="/A176635/b176635.txt">Table of n, a(n) for n = 0..1000</a>
%H A176635 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -8).
%F A176635 a(n) = 64*4^n-7*2^n.
%F A176635 G.f.: (57-100*x)/((1-2*x)*(1-4*x)).
%t A176635 CoefficientList[Series[(57 - 100 x)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)
%t A176635 LinearRecurrence[{6,-8},{57,242},30] (* _Harvey P. Dale_, Jun 08 2016 *)
%o A176635 (PARI) {m=21; v=concat([57, 242], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]); v}
%o A176635 (Magma) [64*4^n-7*2^n: n in [0..25]]; // _Vincenzo Librandi_, Sep 24 2013
%Y A176635 Cf. A075253 (Reverse and Add trajectory of 77 in base 2), A176632, A176633, A176634, A176636 (repeat 57, 71), A171472.
%K A176635 nonn
%O A176635 0,1
%A A176635 _Klaus Brockhaus_, Apr 22 2010