|
%I #10 Sep 08 2022 08:45:53
%S 83,708,2952,12048,48672,195648,784512,3141888,12575232,50316288,
%T 201295872,805244928,3221102592,12884656128,51539116032,206157447168,
%U 824631754752,3298530951168,13194131668992,52776542404608
%N a(n) = 6*a(n-1)-8*a(n-2) for n > 2; a(0) = 83, a(1) = 708, a(2) = 2952.
%C Related to Reverse and Add trajectory of 77 in base 2: a(n) = A075253(4*n+1)/2, i.e., one half of second quadrisection of A075253.
%H Vincenzo Librandi, <a href="/A176633/b176633.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) = 6*(32*4^n-5*2^n) for n > 0, a(1) = 83.
%F G.f.: (83+210*x-632*x^2)/((1-2*x)*(1-4*x)).
%F G.f. for the sequence starting at a(1): 12*x*(59-108*x)/((1-2*x)*(1-4*x)).
%t CoefficientList[Series[(83 + 210 x - 632 x^2)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)
%t LinearRecurrence[{6,-8},{83,708,2952},30] (* _Harvey P. Dale_, Apr 08 2019 *)
%o (PARI) {m=20; v=concat([83, 708, 2952], vector(m-3)); for(n=4, m, v[n]=6*v[n-1]-8*v[n-2]); v}
%o (Magma) [83] cat [6*(32*4^n-5*2^n): n in [1..25]]; // _Vincenzo Librandi_, Sep 24 2013
%Y Cf. A075253 (Reverse and Add trajectory of 77 in base 2), A176632, A176634, A176635, A171470.
%K nonn
%O 0,1
%A _Klaus Brockhaus_, Apr 22 2010
|
