A174316 Sequence defined by a(0)=a(1)=a(2)=1, a(3)=2, a(4)=6 and the formula a(n)=2^(n-2)+2 for n>=5.

1, 1, 1, 2, 6, 10, 18, 34, 66, 130, 258, 514, 1026, 2050, 4098, 8194, 16386, 32770, 65538, 131074, 262146, 524290, 1048578, 2097154, 4194306, 8388610, 16777218, 33554434, 67108866, 134217730, 268435458, 536870914, 1073741826, 2147483650

Offset: 0

Author

Richard Choulet, Mar 15 2010

Keywords

• nonn
• easy
• changed

Examples

			a(5)=2^3+2=10. a(6)=2^4+2=18.
		

Crossrefs

Cf. A052548, A174314.

Programs

Maple

taylor(((1+z^3+4*z^4-4*z^5)/(1-z))+((8*z^5)/(1-2*z)),z=0,50); v(0):=1:v(1):=1:v(2):=1:v(3):=2:v(4):=6: for n from 5 to 50 do v(n):=2^(n-2)+2:od:seq(v(n),n=0..50);

Mathematica

CoefficientList[Series[(1 + z + z^2 + 2*z^3 + 6*z^4 + ((2*z^5)/(1 - z)) + ((2*z)^5/(4*(1 - 2*z)))), {z, 0, 50}], z] (* Wesley Ivan Hurt, Sep 05 2025 *)

Formula

G.f.: (1+x+x^2+2*x^3+6*x^4+((2*x^5)/(1-x))+((2*x)^5/(4*(1-2*x)))).

a(n) = A052548(n-2), n>3. - R. J. Mathar, Feb 29 2016