A216871 16k^2-16k-4 interleaved with 16k^2+4 for k>=0.

-4, 4, -4, 20, 28, 68, 92, 148, 188, 260, 316, 404, 476, 580, 668, 788, 892, 1028, 1148, 1300, 1436, 1604, 1756, 1940, 2108, 2308, 2492, 2708, 2908, 3140, 3356, 3604, 3836, 4100, 4348, 4628, 4892, 5188, 5468, 5780, 6076, 6404, 6716, 7060, 7388, 7748, 8092

Offset

0,1

Comments

The sequence (the third 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 four smaller interleaved sequences where one of them has the formula above and a second interleaved sequences having the formulas (16n^2-24n+1) and (16n^2-6n+5). This interleaved sequence is A214393. The fourth interleaved sequence in the group has the formulas (16n^2-8n-7) and (16n^2+2n+5) and it is A214405. There are a total of four sequences in this family.

Links

Table of n, a(n) for n=0..46.

Eddie Gutierrez New Interleaved Sequences Part C on oddwheel.com, Section B1 Line No. 23 (square_sequencesIII.html) Part C

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

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

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

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

a(n) = 4*A214345(n-3) with A214345(-3)=-1, A214345(-2)=1, A214345(-1)=-1. (End)

Mathematica

Flatten[Table[{16 n^2 - 16 n - 4, 16 n^2 + 4}, {n, 0, 23}]] (* Bruno Berselli, Sep 26 2012 *)
LinearRecurrence[{2, 0, -2, 1}, {-4, 4, -4, 20}, 50] (* Harvey P. Dale, Dec 09 2015 *)

Prog

(Magma) &cat[[16*k^2-16*k-4, 16*k^2+4]: k in [0..23]]; // Bruno Berselli, Sep 27 2012
(PARI) vector(47, n, k=(n-1)\2; if(n%2, 16*k^2-16*k-4, 16*k^2+4)) \\ Bruno Berselli, Sep 28 2012

Crossrefs

Cf. A178218, A214345, A214393, A214405, A216876.

Sequence in context: A131946 A034896 A320970 * A120914 A303397 A024949

Adjacent sequences: A216868 A216869 A216870 * A216872 A216873 A216874

Keyword

sign,easy

Author

Eddie Gutierrez, Sep 18 2012

Extensions

Definition rewritten by Bruno Berselli, Oct 25 2012

Status

approved