A216865 16k^2-32k+8 interleaved with 16k^2-16k+8 for k>=0.

8, 8, -8, 8, 8, 40, 56, 104, 136, 200, 248, 328, 392, 488, 568, 680, 776, 904, 1016, 1160, 1288, 1448, 1592, 1768, 1928, 2120, 2296, 2504, 2696, 2920, 3128, 3368, 3592, 3848, 4088, 4360, 4616, 4904, 5176, 5480, 5768, 6088, 6392, 6728, 7048, 7400, 7736

Offset

0,1

Comments

The sequence (the first 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

G.f.: 8*(1-x-3*x^2+5*x^3)/((1+x)*(1-x)^3). [Bruno Berselli, Sep 30 2012]

a(n) = 2*(2*n*(n-4)-3*(-1)^n+7). [Bruno Berselli, Sep 30 2012]

a(n) = 8*A178218(n-3) with A178218(-3)=1, A178218(-2)=1, A178218(-1)=-1, A178218(0)=1. [Bruno Berselli, Oct 01 2012]

Mathematica

Flatten[Table[{16 n^2 - 32 n + 8, 16 n^2 - 16 n + 8}, {n, 0, 23}]] (* Bruno Berselli, Sep 30 2012 *)

Prog

(Magma) &cat[[16*k^2-32*k+8, 16*k^2-16*k+8]: k in [0..23]]; // Bruno Berselli, Oct 01 2012
(PARI) vector(47, n, k=(n-1)\2; if(n%2, 16*k^2-32*k+8, 16*k^2-16*k+8)) \\ Bruno Berselli, Oct 01 2012

Crossrefs

Cf. A178218, A214345, A214393, A214405, A216844, A216875, A216876.

Sequence in context: A088841 A165925 A165926 * A216412 A166082 A145446

Adjacent sequences: A216862 A216863 A216864 * A216866 A216867 A216868

Keyword

sign,easy

Author

Eddie Gutierrez, Sep 18 2012

Extensions

Definition rewritten by Bruno Berselli, Oct 25 2012

Status

approved