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%I #11 Jun 20 2023 14:23:17
%S 89,519,2063,8223,32831,131199,524543,2097663,8389631,33556479,
%T 134221823,536879103,2147500031,8589967359,34359803903,137439084543,
%U 549756076031,2199023779839,8796094070783,35184374185983
%N a(n) = 6*a(n-1)-8*a(n-2)-3 for n > 2; a(0) = 89, a(1) = 519, a(2) = 2063.
%C Related to Reverse and Add trajectory of 77 in base 2: a(n)= A075253(4*n+2)/3, i.e., one third of third quadrisection of A075253.
%H Vincenzo Librandi, <a href="/A176634/b176634.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).
%F a(n) = 128*4^n+4*2^n-1 for n > 0, a(1) = 89.
%F G.f.: (89-104*x-324*x^2+336*x^3)/((1-x)*(1-2*x)*(1-4*x)).
%F G.f. for the sequence starting at a(1): x*(519-1570*x+1048*x^2)/((1-x)* (1-2*x)*(1-4*x)).
%t CoefficientList[Series[(89 - 104 x - 324 x^2 + 336 x^3)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)
%t LinearRecurrence[{7,-14,8},{89,519,2063,8223},20] (* _Harvey P. Dale_, Jun 20 2023 *)
%o (PARI) {m=20; v=concat([89, 519, 2063], vector(m-3)); for(n=4, m, v[n]=6*v[n-1]-8*v[n-2]-3); v}
%o (Magma) [89] cat [128*4^n+4*2^n-1: n in [1..25]]; // _Vincenzo Librandi_, Sep 24 2013
%Y Cf. A075253 (Reverse and Add trajectory of 77 in base 2), A176632, A176633, A176635.
%K nonn
%O 0,1
%A _Klaus Brockhaus_, Apr 22 2010
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