A176635 a(n) = 6*a(n-1)-8*a(n-2) for n > 1; a(0) = 57, a(1) = 242.

57, 242, 996, 4040, 16272, 65312, 261696, 1047680, 4192512, 16773632, 67101696, 268421120, 1073713152, 4294909952, 17179754496, 68719247360, 274877448192, 1099510710272, 4398044676096, 17592182374400, 70368736837632

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+3)/12, i.e., one twelfth of fourth quadrisection of A075253.

Second binomial transform of 57 followed by 128*A000079.

Third binomial transform of A176636.

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, A176633, A176634, A176636 (repeat 57, 71), A171472.

Programs

Magma

[64*4^n-7*2^n: n in [0..25]]; // Vincenzo Librandi, Sep 24 2013

Mathematica

CoefficientList[Series[(57 - 100 x)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)
LinearRecurrence[{6,-8},{57,242},30] (* Harvey P. Dale, Jun 08 2016 *)

PARI

{m=21; v=concat([57, 242], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]); v}

Formula

a(n) = 64*4^n-7*2^n.

G.f.: (57-100*x)/((1-2*x)*(1-4*x)).