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A216844 4k^2-8k+2 interleaved with 4k^2-4k+2 for k>=0. 2
2, 2, -2, 2, 2, 10, 14, 26, 34, 50, 62, 82, 98, 122, 142, 170, 194, 226, 254, 290, 322, 362, 398, 442, 482, 530, 574, 626, 674, 730, 782, 842, 898, 962, 1022, 1090, 1154, 1226, 1294, 1370, 1442, 1522, 1598, 1682, 1762, 1850, 1934, 2026, 2114, 2210, 2302, 2402 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
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.
LINKS
Eddie Gutierrez New Interleaved Sequences Part A on oddwheel.com, Section B1 Line No. 21 (square_sequencesI.html) Part A
FORMULA
G.f.: 2*(1-x-3*x^2+5*x^3)/((1+x)*(1-x)^3). [Bruno Berselli, Sep 30 2012]
a(n) = (1/2)*(2*n*(n-4)-3*(-1)^n+7). [Bruno Berselli, Sep 30 2012]
a(n) = 2*A178218(n-3) with A178218(-3)=1, A178218(-2)=1, A178218(-1)=-1, A178218(0)=1. [Bruno Berselli, Oct 01 2012]
MATHEMATICA
Flatten[Table[{4 n^2 - 8 n + 2, 4 n^2 - 4 n + 2}, {n, 0, 25}]] (* Bruno Berselli, Sep 30 2012 *)
LinearRecurrence[{2, 0, -2, 1}, {2, 2, -2, 2}, 60] (* Harvey P. Dale, Jul 18 2020 *)
PROG
(Magma) &cat[[4*k^2-8*k+2, 4*k^2-4*k+2]: k in [0..25]]; // Bruno Berselli, Sep 30 2012
CROSSREFS
Sequence in context: A334511 A291944 A253633 * A088050 A260725 A058005
KEYWORD
sign,easy
AUTHOR
Eddie Gutierrez, Sep 17 2012
EXTENSIONS
Definition rewritten by Bruno Berselli, Oct 25 2012
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)