A163839 a(n) = (2^n-1)*4^(2*n-1).

0, 4, 192, 7168, 245760, 8126464, 264241152, 8522825728, 273804165120, 8778913153024, 281200098803712, 9002801208229888, 288160007407534080, 9222246136947933184, 295129890780843343872, 9444444735363138715648, 302226843217638866288640, 9671332769940738559442944

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (48,-512).

Formula

a(n) = 48*a(n-1) - 512*a(n-2) for n > 1; a(0) = 0, a(1) = 4.

G.f.: 4*x/((1-16*x)*(1-32*x)).

E.g.f.: (exp(32*x) - exp(16*x))/4. G. C. Greubel, Aug 05 2017

Example

a(2) = (2^2-1)*4^(2*2-1) = 3*4^3 = 192.

Mathematica

Table[(2^n-1)4^(2n-1), {n, 0, 30}] (* or *) LinearRecurrence[{48, -512}, {0, 4}, 30] (* Harvey P. Dale, Jan 22 2016 *)

Prog

(Magma) [ (2^n-1)*4^(2*n-1): n in [0..15] ];
(PARI) x='x+O('x^50); concat([0], Vec(4*x/((1-16*x)*(1-32*x)))) \\ G. C. Greubel, Aug 05 2017
(Python)
def A163839(n): return (1<<n)-1<<(n<<2)-2 if n else 0 # Chai Wah Wu, Mar 14 2024

Crossrefs

Cf. A000079 (powers of 2), A000302 (powers of 4).

Sequence in context: A355613 A172809 A123116 * A012015 A012102 A274304

Adjacent sequences: A163836 A163837 A163838 * A163840 A163841 A163842

Keyword

nonn,easy

Author

Klaus Brockhaus, Aug 05 2009

Status

approved