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

0,1

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

Table of n, a(n) for n=0..45.

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).

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)

Mathematica

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

Prog

(Magma) &cat[[20*k^2-20*k-5, 20*k^2+5]: k in [0..22]]; // Bruno Berselli, Sep 27 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
(Maxima) A216876(n):=(5/2)*(2*n*(n-2)-3*(-1)^n+1)$
makelist(A216876(n), n, 0, 30); /* Martin Ettl, Nov 01 2012 */

Crossrefs

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

Sequence in context: A365368 A098526 A262122 * A019162 A024951 A092519

Adjacent sequences: A216873 A216874 A216875 * A216877 A216878 A216879

Keyword

sign,easy

Author

Eddie Gutierrez, Sep 18 2012

Extensions

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

Definition rewritten by Bruno Berselli, Oct 25 2012

Status

approved