A176633 a(n) = 6*a(n-1)-8*a(n-2) for n > 2; a(0) = 83, a(1) = 708, a(2) = 2952.

83, 708, 2952, 12048, 48672, 195648, 784512, 3141888, 12575232, 50316288, 201295872, 805244928, 3221102592, 12884656128, 51539116032, 206157447168, 824631754752, 3298530951168, 13194131668992, 52776542404608

Offset: 0

Author

Klaus Brockhaus, Apr 22 2010

Keywords

• nonn

Comments

Related to Reverse and Add trajectory of 77 in base 2: a(n) = A075253(4*n+1)/2, i.e., one half of second quadrisection of A075253.

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. A075253 (Reverse and Add trajectory of 77 in base 2), A176632, A176634, A176635, A171470.

Programs

Magma

[83] cat [6*(32*4^n-5*2^n): n in [1..25]]; // Vincenzo Librandi, Sep 24 2013

Mathematica

CoefficientList[Series[(83 + 210 x - 632 x^2)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)
LinearRecurrence[{6,-8},{83,708,2952},30] (* Harvey P. Dale, Apr 08 2019 *)

PARI

{m=20; v=concat([83, 708, 2952], vector(m-3)); for(n=4, m, v[n]=6*v[n-1]-8*v[n-2]); v}

Formula

a(n) = 6*(32*4^n-5*2^n) for n > 0, a(1) = 83.

G.f.: (83+210*x-632*x^2)/((1-2*x)*(1-4*x)).

G.f. for the sequence starting at a(1): 12*x*(59-108*x)/((1-2*x)*(1-4*x)).