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A216875
20k^2-40k+10 interleaved with 20k^2-20k+10 for k>=0.
2
10, 10, -10, 10, 10, 50, 70, 130, 170, 250, 310, 410, 490, 610, 710, 850, 970, 1130, 1270, 1450, 1610, 1810, 1990, 2210, 2410, 2650, 2870, 3130, 3370, 3650, 3910, 4210, 4490, 4810, 5110, 5450, 5770, 6130, 6470, 6850, 7210, 7610, 7990, 8410, 8810, 9250, 9670
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 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.
LINKS
Eddie Gutierrez New Interleaved Sequences Part E on oddwheel.com Section B1 Line No. 25 (square_sequencesV.html) Part E.
FORMULA
Contribution from Bruno Berselli, Sep 27 2012: (Start)
G.f.: 10*(1-x-3*x^2+5*x^3)/((1+x)*(1-x)^3).
a(n) = (5/2)*(2*n*(n-4)-3*(-1)^n+7).
a(n) = 10*A178218(n-3) with A178218(-3)=1, A178218(-2)=1, A178218(-1)=-1, A178218(0)=1. (End)
MATHEMATICA
Flatten[Table[{20 n^2 - 40 n + 10, 20 n^2 - 20 n + 10}, {n, 0, 23}]] (* Bruno Berselli, Sep 27 2012 *)
LinearRecurrence[{2, 0, -2, 1}, {10, 10, -10, 10}, 60] (* Harvey P. Dale, Sep 18 2020 *)
PROG
(Magma) &cat[[20*k^2-40*k+10, 20*k^2-20*k+10]: k in [0..23]]; // Bruno Berselli, Sep 27 2012
(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
CROSSREFS
Sequence in context: A245403 A091837 A316650 * A166710 A211872 A178166
KEYWORD
sign,easy
AUTHOR
Eddie Gutierrez, Sep 18 2012
EXTENSIONS
Definition rewritten by Bruno Berselli, Oct 25 2012
STATUS
approved