A134136 a(n) = 2*a(n-2) + 4*a(n-3), with initial terms 0, 1, 1.

0, 1, 1, 2, 6, 8, 20, 40, 72, 160, 304, 608, 1248, 2432, 4928, 9856, 19584, 39424, 78592, 157184, 314880, 628736, 1258496, 2516992, 5031936, 10067968, 20131840, 40263680, 80535552, 161054720, 322125824, 644251648, 1288470528, 2577006592, 5153947648, 10307895296

Offset

0,4

Links

Robert Israel, Table of n, a(n) for n = 0..2991

Index entries for linear recurrences with constant coefficients, signature (0,2,4).

Formula

a(n) = (6*2^n - (3+i)*(-1+i)^n - (3-i)*(-1-i)^n)/20. - Ivan Neretin, May 27 2015

G.f.: (x^2+x)/(1-2*x^2-4*x^3). - Robert Israel, May 27 2015

Maple

f:= gfun:-rectoproc({a(n)=2*a(n-2)+4*a(n-3), a(0)=0, a(1)=1, a(2)=1}, a(n), remember):
seq(f(n), n=0..100); # Robert Israel, May 27 2015

Mathematica

Nest[Append[#, 2 #[[-2]] + 4 #[[-3]]] &, {0, 1, 1}, 15] (* Ivan Neretin, May 27 2015 *)
CoefficientList[Series[x (1 + x)/((1 - 2 x) (2 x^2 + 2 x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, May 28 2015 *)

Prog

(Magma) [n le 3 select Floor(n/2) else 2*Self(n-2)+4*Self(n-3): n in [1..40]]; // Vincenzo Librandi, May 28 2015

Crossrefs

Cf. A134654.

Sequence in context: A064713 A162213 A100358 * A185165 A289892 A289095

Adjacent sequences: A134133 A134134 A134135 * A134137 A134138 A134139

Keyword

nonn,easy

Author

Paul Curtz, Jan 29 2008

Extensions

More terms from Robert Israel, May 27 2015

Status

approved