A177682 - OEIS

%I #19 Apr 18 2024 06:12:03

%S 179,1571,12511,155403,572951,2194479,8583263,33943743,134996351,

%T 538428159,2150598143,8596163583,34372196351,137463869439,

%U 549805645823,2199122919423,8796292349951,35184770744319,140738285666303

%N a(n) = 6*a(n-1)-8*a(n-2)-3 for n > 4; a(0)=179, a(1)=1571, a(2)=12511, a(3)=155403, a(4)=572951.

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

%H Vincenzo Librandi, <a href="/A177682/b177682.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) = 2*4^(n+5)+6083*2^(n-1)-1 for n > 2.

%F G.f.: (179+318*x+4020*x^2+88388*x^3-352284*x^4+259376*x^5) / ((1-x)*(1-2*x)*(1-4*x)).

%F G.f. for the sequence starting at a(3): x^3*(155403-514870*x+359464*x^2) / ((1-x)*(1-2*x)*(1-4*x)).

%t Join[{179,1571,12511},LinearRecurrence[{7,-14,8},{155403,572951,2194479},20]] (* _Harvey P. Dale_, Oct 06 2011 *)

%t CoefficientList[Series[(179 + 318 x + 4020 x^2 + 88388 x^3 - 352284 x^4 + 259376 x^5)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)

%o (PARI) {m=19; v=concat([179, 1571, 12511, 155403, 572951], vector(m-5)); for(n=6 ,m, v[n]=6*v[n-1]-8*v[n-2]-3); v}

%o (Magma) [179, 1571, 12511] cat [2*4^(n+5)+6083*2^(n-1)-1: n in [3..25]]; // _Vincenzo Librandi_, Sep 24 2013

%Y Cf. A077076 (Reverse and Add trajectory of 537 in base 2), A177683, A177684, A177685.

%K nonn,easy

%O 0,1

%A _Klaus Brockhaus_, May 12 2010