A171472 a(n) = 6*a(n-1) - 8*a(n-2) for n > 1; a(0) = 7, a(1) = 30.

7, 30, 124, 504, 2032, 8160, 32704, 130944, 524032, 2096640, 8387584, 33552384, 134213632, 536862720, 2147467264, 8589901824, 34359672832, 137438822400, 549755551744, 2199022731264, 8796091973632, 35184369991680

Offset: 0

Author

Klaus Brockhaus, Dec 09 2009

Keywords

• nonn
• easy

Comments

Related to Reverse and Add trajectory of 22 in base 2: A061561(4*n+2) = 12*a(n).

Third binomial transform of A010729.

a(n) in base 2 is n+3 1s followed by n 0s. - Hussam al-Homsi, Oct 12 2021

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (6,-8).

Crossrefs

Cf. A061561, A010729 (repeat 7, 9), A171470, A171471, A171473, A171499.

Programs

Magma

[8*4^n-2^n: n in [0..30]]; // Vincenzo Librandi, May 31 2011

Mathematica

LinearRecurrence[{6,-8},{7,30},30] (* Harvey P. Dale, Sep 01 2016 *)

PARI

{m=22; v=concat([7, 30], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]); v}

Formula

a(n) = 8*4^n-2^n.

G.f.: (7-12*x)/((1-2*x)*(1-4*x)).

a(n) = A171499(n+1)/2. - Hussam al-Homsi, Jun 06 2021

E.g.f.: exp(2*x)*(8*exp(2*x) - 1). - Stefano Spezia, Sep 27 2023