A177685 a(n) = 6*a(n-1)-8*a(n-2) for n > 4; a(0)=603, a(1)=4731, a(2)=58834, a(3)=254204, a(4)=1032696.

603, 4731, 58834, 254204, 1032696, 4162544, 16713696, 66981824, 268181376, 1073233664, 4293950976, 17177836544, 68715411456, 274869776384, 1099495366656, 4398013988864, 17592120999936, 70368614088704

Offset: 0

Author

Klaus Brockhaus, May 12 2010

Keywords

• nonn

Comments

Related to Reverse and Add trajectory of 537 in base 2: a(n) = A077076(4*n+3)/6, i.e., one sixth of fourth 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, A177683, A177684.

Programs

Magma

[603, 4731, 58834] cat [4^(n+6)-1985*2^(n-1): n in [3..25]]; // Vincenzo Librandi, Sep 24 2013

Mathematica

CoefficientList[Series[(603 + 1113 x + 35272 x^2 - 60952 x^3 - 21856 x^4)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)
LinearRecurrence[{6,-8},{603,4731,58834,254204,1032696},20] (* Harvey P. Dale, May 26 2019 *)

PARI

{m=18; v=concat([603, 4731, 58834, 254204, 1032696], vector(m-5)); for(n=6 ,m, v[n]=6*v[n-1]-8*v[n-2]); v}

Formula

a(n) = 4^(n+6)-1985*2^(n-1) for n > 2.

G.f.: (603+1113*x+35272*x^2-60952*x^3-21856*x^4) / ((1-2*x)*(1-4*x)).

G.f. for the sequence starting at a(3): 4*x^3*(63551-123132*x) / ((1-2*x)*(1-4*x)).