A083885 (4^n+2^n+0^n+(-2)^n)/4

1, 1, 6, 16, 72, 256, 1056, 4096, 16512, 65536, 262656, 1048576, 4196352, 16777216, 67117056, 268435456, 1073774592, 4294967296, 17180000256, 68719476736, 274878431232, 1099511627776, 4398048608256, 17592186044416, 70368752566272

Offset

0,3

Comments

Binomial transform of A083884.

Links

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

Index entries for linear recurrences with constant coefficients, signature (4,4,-16).

Formula

a(n) = (4^n+2^n+0^n+(-2)^n)/4.

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

E.g.f.: exp(4*x)+exp(2*x)+exp(0)+exp(-2*x).

A007814(a(n)) = A022998(n-1). - Ralf Stephan, Feb 14 2004

a(0)=1, a(1)=1, a(2)=6, a(3)=16, a(n)=4*a(n-1)+4*a(n-2)-16*a(n-3) [From Harvey P. Dale, Dec 12 2011]

Mathematica

Join[{1}, Table[(4^n+2^n+(-2)^n)/4, {n, 30}]] (* or *) Join[{1}, LinearRecurrence[ {4, 4, -16}, {1, 6, 16}, 30]] (* Harvey P. Dale, Dec 12 2011 *)

Prog

(Magma) [(4^n+2^n+0^n+(-2)^n)/4: n in [0..20]]; // Vincenzo Librandi, Jun 16 2011

Crossrefs

Sequence in context: A118640 A277747 A142704 * A350649 A211954 A230942

Adjacent sequences: A083882 A083883 A083884 * A083886 A083887 A083888

Keyword

easy,nonn

Author

Paul Barry, May 09 2003

Status

approved