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%I #40 Sep 08 2022 08:46:03
%S 2,2,-2,2,2,10,14,26,34,50,62,82,98,122,142,170,194,226,254,290,322,
%T 362,398,442,482,530,574,626,674,730,782,842,898,962,1022,1090,1154,
%U 1226,1294,1370,1442,1522,1598,1682,1762,1850,1934,2026,2114,2210,2302,2402
%N 4k^2-8k+2 interleaved with 4k^2-4k+2 for k>=0.
%C The sequence 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 (4n^2 + 4n -1) and (4n^2+1). The latter interleaved sequence is A214345.
%H Eddie Gutierrez <a href="http://www.oddwheel.com/square_sequencesI.html">New Interleaved Sequences Part A</a> on oddwheel.com, Section B1 Line No. 21 (square_sequencesI.html) Part A
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F G.f.: 2*(1-x-3*x^2+5*x^3)/((1+x)*(1-x)^3). [_Bruno Berselli_, Sep 30 2012]
%F a(n) = (1/2)*(2*n*(n-4)-3*(-1)^n+7). [_Bruno Berselli_, Sep 30 2012]
%F a(n) = 2*A178218(n-3) with A178218(-3)=1, A178218(-2)=1, A178218(-1)=-1, A178218(0)=1. [_Bruno Berselli_, Oct 01 2012]
%t Flatten[Table[{4 n^2 - 8 n + 2, 4 n^2 - 4 n + 2}, {n, 0, 25}]] (* _Bruno Berselli_, Sep 30 2012 *)
%t LinearRecurrence[{2,0,-2,1},{2,2,-2,2},60] (* _Harvey P. Dale_, Jul 18 2020 *)
%o (Magma) &cat[[4*k^2-8*k+2, 4*k^2-4*k+2]: k in [0..25]]; // _Bruno Berselli_, Sep 30 2012
%Y Cf. A178218, A214345, A214393, A214405, A216576.
%K sign,easy
%O 0,1
%A _Eddie Gutierrez_, Sep 17 2012
%E Definition rewritten by _Bruno Berselli_, Oct 25 2012
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