A176632 - OEIS

%I #14 Sep 08 2022 08:45:53

%S 77,897,3333,12813,50205,198717,790653,3154173,12599805,50365437,

%T 201394173,805441533,3221495805,12885442557,51540688893,206160592893,

%U 824638046205,3298543534077,13194156834813,52776592736253

%N a(n) = 6*a(n-1)-8*a(n-2)-9 for n > 2; a(0) = 77, a(1) = 897, a(2) = 3333.

%C Related to Reverse and Add trajectory of 77 in base 2: a(n) = A075253(4*n), i.e., first quadrisection of A075253.

%H Vincenzo Librandi, <a href="/A176632/b176632.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*(64*4^n+22*2^n-1) for n > 0, a(0) = 77.

%F G.f.: (77+358*x-1868*x^2+1424*x^3)/((1-x)*(1-2*x)*(1-4*x)).

%F G.f. for the sequence starting at a(1): 3*x*(299-982*x+680*x^2)/((1-x)* (1-2*x)*(1-4*x)).

%t CoefficientList[Series[(77 + 358 x - 1868 x^2 + 1424 x^3)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)

%t Join[{77},RecurrenceTable[{a[1]==897,a[2]==3333,a[n]==6a[n-1]-8a[n-2]- 9},a[n],{n,20}]] (* _Harvey P. Dale_, May 21 2019 *)

%o (PARI) {m=20; v=concat([77, 897, 3333], vector(m-3)); for(n=4, m, v[n]=6*v[n-1]-8*v[n-2]-9); v}

%o (Magma) [77] cat [3*(64*4^n+22*2^n-1): n in [1..25]]; // _Vincenzo Librandi_, Sep 24 2013

%Y Cf. A075253 (Reverse and Add trajectory of 77 in base 2), A176633, A176634, A176635, A171471.

%K nonn,easy

%O 0,1

%A _Klaus Brockhaus_, Apr 22 2010