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A177845 a(n) = 6*a(n-1)-8*a(n-2)-3 for n > 2; a(0)=775, a(1)=8919, a(2)=34223.

%I A177845 #12 Sep 08 2022 08:45:53
%S A177845 775,8919,34223,133983,530111,2108799,8411903,33601023,134310911,
%T A177845 537057279,2147856383,8590680063,34361229311,137441935359,
%U A177845 549761777663,2199035183103,8796116877311,35184419799039,140737583775743
%N A177845 a(n) = 6*a(n-1)-8*a(n-2)-3 for n > 2; a(0)=775, a(1)=8919, a(2)=34223.
%C A177845 Related to Reverse and Add trajectory of 775 in base 2: a(n) = A077077(4*n+2)/3, i.e. one third of third quadrisection of A077077.
%H A177845 Vincenzo Librandi, <a href="/A177845/b177845.txt">Table of n, a(n) for n = 0..1000</a>
%H A177845 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7, -14, 8).
%F A177845 a(n) = 2*4^(n+5)+91*2^(n+2)-1 for n > 0.
%F A177845 G.f.: (775+3494*x-17360*x^2+13088*x^3) / ((1-x)*(1-2*x)*(1-4*x)).
%F A177845 G.f. for the sequence starting at a(1): x*(8919-28210*x+19288*x^2) / ((1-x)*(1-2*x)*(1-4*x)).
%F A177845 a(0)=775, a(1)=8919, a(2)=34223, a(3)=133983, a(n)=7*a(n-1)-14*a(n-2)+8*a(n-3). - _Harvey P. Dale_, Mar 04 2013
%t A177845 nxt[{a_,b_}]:={b,6b-8a-3}; Join[{775},Transpose[NestList[nxt,{8919,34223},20]][[1]]] (* or *) Join[{775},LinearRecurrence[{7,-14,8},{8919,34223,133983},20]] (* _Harvey P. Dale_, Mar 04 2013 *)
%t A177845 CoefficientList[Series[(775 + 3494 x - 17360 x^2 + 13088 x^3)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)
%o A177845 (PARI) {m=19; v=concat([775, 8919, 34223], vector(m-3)); for(n=4, m, v[n]=6*v[n-1]-8*v[n-2]-3); v}
%o A177845 (Magma) [775] cat [2*4^(n+5)+91*2^(n+2)-1: n in [1..25]]; // _Vincenzo Librandi_, Sep 24 2013
%Y A177845 Cf. A077077 (Reverse and Add trajectory of 775 in base 2), A177843, A177844, A177846.
%K A177845 nonn,easy
%O A177845 0,1
%A A177845 _Klaus Brockhaus_, May 14 2010