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 A216871 16k^2-16k-4 interleaved with 16k^2+4 for k>=0. 1
 -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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified March 31 19:37 EDT 2020. Contains 333151 sequences. (Running on oeis4.)