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A216853 18k^2-12k-7 interleaved with 18k^2+6k+5 for k>=0.

%I A216853 #29 Sep 08 2022 08:46:03
%S A216853 -7,5,-1,29,41,89,119,185,233,317,383,485,569,689,791,929,1049,1205,
%T A216853 1343,1517,1673,1865,2039,2249,2441,2669,2879,3125,3353,3617,3863,
%U A216853 4145,4409,4709,4991,5309,5609,5945,6263,6617,6953,7325,7679,8069,8441,8849
%N A216853 18k^2-12k-7 interleaved with 18k^2+6k+5 for k>=0.
%C A216853 The sequence (the third in the family) is present as a family of single interleaved sequence of which there are many which are separated or factored out to give individual sequences. The larger sequence produces two smaller interleaved sequences where one of them  has the formulas above and the other interleaved sequence has the formulas (18n^2-24n-1) and  (18n^2-6n+5). The latter interleaved sequence is A214493. There are three sequences in this family.
%H A216853 Eddie Gutierrez <a href="http://oddwheel.com/square_sequencesII.html"> New Interleaved Sequences Part B</a>  on oddwheel.com, Section B1 Line No. 22 (square_sequencesII.html) Part B
%H A216853 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A216853 G.f.: -(7-19*x+11*x^2-17*x^3)/((1+x)*(1-x)^3). - _Bruno Berselli_, Oct 05 2012
%F A216853 a(n) = (6*n*(3*n-4)-27*(-1)^n-1)/4. - _Bruno Berselli_, Oct 05 2012
%t A216853 Flatten[Table[{18 n^2 - 12 n - 7, 18 n^2 + 6 n + 5}, {n, 0, 22}]] (* _Bruno Berselli_, Oct 05 2012 *)
%o A216853 (Magma) &cat[[18*k^2-12*k-7, 18*k^2+6*k+5]: k in [0..22]]; // _Bruno Berselli_, Oct 05 2012
%o A216853 (PARI) vector(46, n, k=(n-1)\2; if(n%2, 18*k^2-12*k-7, 18*k^2+6*k+5)) \\ _Bruno Berselli_, Oct 05 2012
%Y A216853 Cf. A178218, A214345, A214393, A214405, A216876.
%K A216853 sign,easy
%O A216853 0,1
%A A216853 _Eddie Gutierrez_, Sep 17 2012
%E A216853 Definition rewritten by _Bruno Berselli_, Oct 25 2012