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%I #30 Sep 08 2022 08:46:03
%S 10,10,-10,10,10,50,70,130,170,250,310,410,490,610,710,850,970,1130,
%T 1270,1450,1610,1810,1990,2210,2410,2650,2870,3130,3370,3650,3910,
%U 4210,4490,4810,5110,5450,5770,6130,6470,6850,7210,7610,7990,8410,8810,9250,9670
%N 20k^2-40k+10 interleaved with 20k^2-20k+10 for k>=0.
%C 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 two smaller interleaved sequences where one of them has the formula above and a second interleaved sequence. There are a total of two sequences in this family.
%H Eddie Gutierrez <a href="http://www.oddwheel.com/square_sequencesV.html">New Interleaved Sequences Part E</a> on oddwheel.com Section B1 Line No. 25 (square_sequencesV.html) Part E.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F Contribution from _Bruno Berselli_, Sep 27 2012: (Start)
%F G.f.: 10*(1-x-3*x^2+5*x^3)/((1+x)*(1-x)^3).
%F a(n) = (5/2)*(2*n*(n-4)-3*(-1)^n+7).
%F a(n) = 10*A178218(n-3) with A178218(-3)=1, A178218(-2)=1, A178218(-1)=-1, A178218(0)=1. (End)
%t Flatten[Table[{20 n^2 - 40 n + 10, 20 n^2 - 20 n + 10}, {n, 0, 23}]] (* _Bruno Berselli_, Sep 27 2012 *)
%t LinearRecurrence[{2,0,-2,1},{10,10,-10,10},60] (* _Harvey P. Dale_, Sep 18 2020 *)
%o (Magma) &cat[[20*k^2-40*k+10, 20*k^2-20*k+10]: k in [0..23]]; // _Bruno Berselli_, Sep 27 2012
%o (PARI) vector(47, n, k=(n-1)\2; if(n%2, 20*k^2-40*k+10, 20*k^2-20*k+10)) \\ _Bruno Berselli_, Sep 28 2012
%K sign,easy
%O 0,1
%A _Eddie Gutierrez_, Sep 18 2012
%E Definition rewritten by _Bruno Berselli_, Oct 25 2012
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