A177684 - OEIS

%I #16 Oct 13 2024 19:44:16

%S 633,4809,46041,277767,1079823,4256799,16902207,67358847,268935423,

%T 1074741759,4296967167,17183868927,68727476223,274893905919,

%U 1099543625727,4398110507007,17592314036223,70369000161279

%N a(n) = 6*a(n-1)-8*a(n-2)-3 for n > 4; a(0)=633, a(1)=4809, a(2)=46041, a(3)=277767, a(4)=1079823.

%C Related to Reverse and Add trajectory of 537 in base 2: a(n) = A077076(4*n+2)/3, i.e., one third of third quadrisection of A077076.

%H Vincenzo Librandi, <a href="/A177684/b177684.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) = 4^(n+6)+1953*2^n-1 for n > 2.

%F G.f.: 3*(211+126*x+7080*x^2+5914*x^3-86148*x^4+72816*x^5) / ((1-x)*(1-2*x)*(1-4*x)).

%F G.f. for the sequence starting at a(3): 3*x^3*(92589-288182*x+195592*x^2) / ((1-x)*(1-2*x)*(1-4*x)).

%F a(0)=633, a(1)=4809, a(2)=46041, a(3)=277767, a(4)=1079823, a(5)=4256799, a(n)=7*a(n-1)-14*a(n-2)+8*a(n-3). - _Harvey P. Dale_, May 03 2012

%t Join[{633,4809,46041},RecurrenceTable[{a[3]==277767,a[4]==1079823,a[n] == 6a[n-1]-8a[n-2]-3},a,{n,20}]] (* or *) Join[{633,4809,46041}, LinearRecurrence[ {7,-14,8},{277767,1079823,4256799},18]] (* _Harvey P. Dale_, May 03 2012 *)

%t CoefficientList[Series[3 (211 + 126 x + 7080 x^2 + 5914 x^3 - 86148 x^4 + 72816 x^5)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)

%o (PARI) {m=18; v=concat([633, 4809, 46041, 277767, 1079823], vector(m-5)); for(n=6 ,m, v[n]=6*v[n-1]-8*v[n-2]-3); v}

%o (Magma) [633, 4809, 46041] cat [4^(n+6)+1953*2^n-1: n in [3..25]]; // _Vincenzo Librandi_, Sep 24 2013

%Y Cf. A077076 (Reverse and Add trajectory of 537 in base 2), A177682, A177683, A177685.

%K nonn,easy

%O 0,1

%A _Klaus Brockhaus_, May 12 2010