A176634 a(n) = 6*a(n-1)-8*a(n-2)-3 for n > 2; a(0) = 89, a(1) = 519, a(2) = 2063.

89, 519, 2063, 8223, 32831, 131199, 524543, 2097663, 8389631, 33556479, 134221823, 536879103, 2147500031, 8589967359, 34359803903, 137439084543, 549756076031, 2199023779839, 8796094070783, 35184374185983

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+2)/3, i.e., one third of third quadrisection of A075253.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Crossrefs

Cf. A075253 (Reverse and Add trajectory of 77 in base 2), A176632, A176633, A176635.

Programs

Magma

[89] cat [128*4^n+4*2^n-1: n in [1..25]]; // Vincenzo Librandi, Sep 24 2013

Mathematica

CoefficientList[Series[(89 - 104 x - 324 x^2 + 336 x^3)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)
LinearRecurrence[{7,-14,8},{89,519,2063,8223},20] (* Harvey P. Dale, Jun 20 2023 *)

PARI

{m=20; v=concat([89, 519, 2063], vector(m-3)); for(n=4, m, v[n]=6*v[n-1]-8*v[n-2]-3); v}

Formula

a(n) = 128*4^n+4*2^n-1 for n > 0, a(1) = 89.

G.f.: (89-104*x-324*x^2+336*x^3)/((1-x)*(1-2*x)*(1-4*x)).

G.f. for the sequence starting at a(1): x*(519-1570*x+1048*x^2)/((1-x)* (1-2*x)*(1-4*x)).