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A163839
a(n) = (2^n-1)*4^(2*n-1).
2
0, 4, 192, 7168, 245760, 8126464, 264241152, 8522825728, 273804165120, 8778913153024, 281200098803712, 9002801208229888, 288160007407534080, 9222246136947933184, 295129890780843343872, 9444444735363138715648, 302226843217638866288640, 9671332769940738559442944
OFFSET
0,2
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
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Aug 05 2009
STATUS
approved