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

Author

Paul Curtz, Jan 29 2008

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 0..2991
• Index entries for linear recurrences with constant coefficients, signature (0,2,4).

Crossrefs

Cf. A038521.

Programs

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

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 *)

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

Extensions

More terms from Robert Israel, May 27 2015