

A216844


4k^28k+2 interleaved with 4k^24k+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
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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

Table of n, a(n) for n=0..51.
Eddie Gutierrez New Interleaved Sequences Part A on oddwheel.com, Section B1 Line No. 21 (square_sequencesI.html) Part A
Index entries for linear recurrences with constant coefficients, signature (2,0,2,1).


FORMULA

G.f.: 2*(1x3*x^2+5*x^3)/((1+x)*(1x)^3). [Bruno Berselli, Sep 30 2012]
a(n) = (1/2)*(2*n*(n4)3*(1)^n+7). [Bruno Berselli, Sep 30 2012]
a(n) = 2*A178218(n3) 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^28*k+2, 4*k^24*k+2]: k in [0..25]]; // Bruno Berselli, Sep 30 2012


CROSSREFS

Cf. A178218, A214345, A214393, A214405, A216576.
Sequence in context: A334511 A291944 A253633 * A088050 A260725 A058005
Adjacent sequences: A216841 A216842 A216843 * A216845 A216846 A216847


KEYWORD

sign,easy


AUTHOR

Eddie Gutierrez, Sep 17 2012


EXTENSIONS

Definition rewritten by Bruno Berselli, Oct 25 2012


STATUS

approved



