A177843 - OEIS

%I #11 Aug 03 2023 10:23:09

%S 775,8919,49581,197469,788157,3149181,12589821,50345469,201354237,

%T 805361661,3221336061,12885123069,51540049917,206159314941,

%U 824635490301,3298538422269,13194146611197,52776572289021,211106260844541

%N a(n) = 6*a(n-1)-8*a(n-2)-9 for n > 3; a(0)=775, a(1)=8919, a(2)=49581, a(3)=197469.

%C Related to Reverse and Add trajectory of 775 in base 2: a(n) = A077077(4*n), i.e. first quadrisection of A077077.

%H Vincenzo Librandi, <a href="/A177843/b177843.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) = 3*4^(n+5)+27*2^(n+2)-3 for n > 1.

%F G.f.: (775+3494*x-2002*x^2-30932*x^3+28656*x^4) / ((1-x)*(1-2*x)*(1-4*x)).

%F G.f. for the sequence starting at a(2): 9*x^2*(5509-16622*x+11112*x^2) / ((1-x)*(1-2*x)*(1-4*x)).

%t CoefficientList[Series[(775 + 3494 x - 2002 x^2 - 30932 x^3 + 28656 x^4)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)

%t LinearRecurrence[{7,-14,8},{775,8919,49581,197469,788157},20] (* _Harvey P. Dale_, Aug 03 2023 *)

%o (PARI) {m=19; v=concat([775, 8919, 49581, 197469], vector(m-4)); for(n=5, m, v[n]=6*v[n-1]-8*v[n-2]-9); v}

%o (Magma) [775, 8919] cat [3*4^(n+5)+27*2^(n+2)-3: n in [2..25]]; // _Vincenzo Librandi_, Sep 24 2013

%Y Cf. A077077 (Reverse and Add trajectory of 775 in base 2), A177844, A177845, A177846.

%K nonn,easy

%O 0,1

%A _Klaus Brockhaus_, May 14 2010