A229135 n * (2 + 2^(2*n - 1)).

0, 4, 20, 102, 520, 2570, 12300, 57358, 262160, 1179666, 5242900, 23068694, 100663320, 436207642, 1879048220, 8053063710, 34359738400, 146028888098, 618475290660, 2611340116006, 10995116277800, 46179488366634, 193514046488620, 809240558043182, 3377699720527920

Offset: 0

Author

Paul Curtz, Sep 15 2013

Keywords

• nonn
• easy

Comments

a(n) mod 9 is periodic: repeat 0, 4, 2, 3, 7, 5, 6, 1, 8.

b(n) = a(n) - n = 0, 3, 18, 99, 516, 2565, 12294,... = A215149(2n)/2.

Examples

			a(0)=0*(2+1/2)=0, a(1)=1*(2+2)=4, a(2)=2*(2+8)=20, a(3)=3*(2+32)=102, a(4)=4*(2+128)=520, a(5)=5*(2+512)=2570.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-33,40,-16).

Crossrefs

Cf. A005843, A052539, A081294, A215149, A228827, A000367, A002445, A123166.

Programs

Magma

[n*(2 + 2^(2*n - 1)): n in [0..30]]; // Vincenzo Librandi, Sep 20 2013

Mathematica

Table[(n (2 + 2^(2 n - 1))), {n, 0, 40}] (* Vincenzo Librandi, Sep 20 2013 *)

PARI

a(n) = n*(2+2^(2*n-1)); \\ Michel Marcus, Sep 16 2013

Formula

a(n) = n + A215149(2n)/2.

a(n) = (A228827(n) - A000367(n))/A002445(n).

a(n) = 2*n*A123166(n).

G.f.: (34*x^3 - 20*x^2 + 4*x)/((1-x)^2*(1-4*x)^2). - Ralf Stephan, Sep 20 2013

Extensions

Better definition by Michel Marcus.

More terms from Vincenzo Librandi, Sep 20 2013