A216876 20k^2-20k-5 interleaved with 20k^2+5 for k=>0.

-5, 5, -5, 25, 35, 85, 115, 185, 235, 325, 395, 505, 595, 725, 835, 985, 1115, 1285, 1435, 1625, 1795, 2005, 2195, 2425, 2635, 2885, 3115, 3385, 3635, 3925, 4195, 4505, 4795, 5125, 5435, 5785, 6115, 6485, 6835, 7225, 7595, 8005, 8395, 8825, 9235, 9685

Offset: 0

Author

Eddie Gutierrez, Sep 18 2012

Keywords

• sign
• easy

Comments

The sequence (the second in the family) is present as a family of single interleaved sequence of which are separated or factored out of the larger sequence to give individual sequences. The larger sequence produces two smaller interleaved sequences where one of them has the formula above and a first interleaved sequence. There are a total of two sequences in this family.

Links

• Eddie Gutierrez New Interleaved Sequences Part E on oddwheel.com, Section B1 Line No. 25 (square_sequencesV.html), Part E.
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Cf. A178218, A214345, A214493, A214393, A214405, A216871.

Programs

Magma

&cat[[20*k^2-20*k-5, 20*k^2+5]: k in [0..22]]; // Bruno Berselli, Sep 27 2012

Mathematica

Flatten[Table[{20*n^2 - 20*n - 5, 20*n^2 + 5}, {n, 0, 30}]] (* T. D. Noe, Sep 26 2012 *)

Maxima

A216876(n):=(5/2)*(2*n*(n-2)-3*(-1)^n+1)$
makelist(A216876(n),n,0,30); /* Martin Ettl, Nov 01 2012 */

PARI

vector(60,n,k=(n-1)\2;if(n%2,20*k^2-20*k-5,20*k^2+5)) \\ Charles R Greathouse IV, Sep 27 2012

Formula

Contribution from Bruno Berselli, Sep 27 2012: (Start)

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

a(n) = (5/2)*(2*n*(n-2)-3*(-1)^n+1).

a(n) = 5*A214345(n-3) with A214345(-3)=-1, A214345(-2)=1, A214345(-1)=-1. (End)

Extensions

More terms from T. D. Noe, Sep 26 2012

Definition rewritten by Bruno Berselli, Oct 25 2012