A177683 a(n) = 6*a(n-1)-8*a(n-2) for n > 4; a(0)=191, a(1)=1587, a(2)=14161, a(3)=123004, a(4)=508152.

191, 1587, 14161, 123004, 508152, 2064880, 8324064, 33425344, 133959552, 536354560, 2146450944, 8587869184, 34355607552, 137430691840, 549739290624, 2198990209024, 8796026929152, 35184239902720, 140737223983104

Offset: 0

Author

Klaus Brockhaus, May 12 2010

Keywords

• nonn
• easy

Comments

Related to Reverse and Add trajectory of 537 in base 2: a(n) = A077076(4*n+1)/6, i.e., one sixth of second quadrisection of A077076.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6, -8).

Crossrefs

Cf. A077076 (Reverse and Add trajectory of 537 in base 2), A177682, A177684, A177685.

Programs

Magma

[191, 1587, 14161] cat [2*4^(n+5)-2017*2^(n-1): n in [3..25]]; // Vincenzo Librandi, Sep 24 2013

Mathematica

Join[{191,1587,14161},Transpose[NestList[{Last[#],6Last[#]-8First[#]}&,{123004,508152},20]][[1]]]  (* Harvey P. Dale, Mar 06 2011 *)
CoefficientList[Series[(191 + 441 x + 6167 x^2 + 50734 x^3 - 116584 x^4)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)
LinearRecurrence[{6,-8},{191,1587,14161,123004,508152},20] (* Harvey P. Dale, Oct 16 2019 *)

PARI

{m=19; v=concat([191, 1587, 14161, 123004, 508152], vector(m-5)); for(n=6 ,m, v[n]=6*v[n-1]-8*v[n-2]); v}

Formula

a(n) = 2*4^(n+5)-2017*2^(n-1) for n > 2.

G.f.: (191+441*x+6167*x^2+50734*x^3-116584*x^4) / ((1-2*x)*(1-4*x)).

G.f. for the sequence starting at a(3): 4*x^3*(30751-57468*x) / ((1-2*x)*(1-4*x)).