A144433 Multiples of 8 interleaved with the sequence of odd numbers >= 3.

8, 3, 16, 5, 24, 7, 32, 9, 40, 11, 48, 13, 56, 15, 64, 17, 72, 19, 80, 21, 88, 23, 96, 25, 104, 27, 112, 29, 120, 31, 128, 33, 136, 35, 144, 37, 152, 39, 160, 41, 168, 43, 176, 45, 184, 47, 192, 49, 200, 51, 208, 53, 216, 55, 224, 57, 232, 59, 240, 61, 248, 63, 256, 65, 264

Offset: 1

Author

Paul Curtz, Oct 04 2008

Keywords

• nonn
• easy

Comments

For n >= 2, these are the numerators of 1/n^2 - 1/(n+1)^2: A061037(4), A061039(5), A061041(6), A061043(7), A061045(8), A061047(9), A061049(10), etc.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

Cf. A120070.

Programs

Magma

[5+3/2*(-1)^(n-1)*(n-1)+3*(-1)^(n-1)+5/2*(n-1): n in [1..70]]; // Vincenzo Librandi, Jul 30 2011

Maple

A144433:=n->(n+1)*4^(n mod 2); seq(A144433(n), n=1..100); # Wesley Ivan Hurt, Nov 27 2013

Mathematica

Table[(n + 1)* 4^Mod[n, 2], {n, 100}] (* Wesley Ivan Hurt, Nov 27 2013 *)

PARI

x='x+O('x^50); Vec( x*(8+3*x-x^3)/((1-x)^2*(1+x)^2)) \\ G. C. Greubel, Sep 19 2018

Formula

a(2*n+1) = A008590(n+1), a(2*n) = A005408(n).

a(2*n+1) + a(2*n+2) = A017281(n+1).

From R. J. Mathar, Apr 01 2009: (Start)

a(n) = 2*a(n-2) - a(n-4).

G.f.: x*(8+3*x-x^3)/((1-x)^2*(1+x)^2). (End)

a(n) = (n + 1) * 4^(n mod 2). - Wesley Ivan Hurt, Nov 27 2013

Extensions

Edited by R. J. Mathar, Apr 01 2009