This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A216852 18k^2-36k+9 interleaved with 18k^2-18k+9 for k>=0. 0
 9, 9, -9, 9, 9, 45, 63, 117, 153, 225, 279, 369, 441, 549, 639, 765, 873, 1017, 1143, 1305, 1449, 1629, 1791, 1989, 2169, 2385, 2583, 2817, 3033, 3285, 3519, 3789, 4041, 4329, 4599, 4905, 5193, 5517, 5823, 6165, 6489, 6849, 7191, 7569, 7929, 8325, 8703 (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 (18n^2-24n+1) and (18n^2-6n+5). The latter interleaved sequence is A214493. There are three sequences in this family. LINKS Eddie Gutierrez New Interleaved Sequences Part B on oddwheel.com, Section B1 Line No. 22 (square_sequencesII.html) Part B Index entries for linear recurrences with constant coefficients, signature (2, 0, -2, 1). FORMULA From Bruno Berselli, Oct 01 2012: (Start) G.f.: 9*(1-x-3*x^2+5*x^3)/((1+x)*(1-x)^3). a(n) = (9/4)*(2*n*(n-4)-3*(-1)^n+7). a(n) = 9*A178218(n-3) with A178218(-3)=1, A178218(-2)=1, A178218(-1)=-1, A178218(0)=1. (End) a(0)=9, a(1)=9, a(2)=-9, a(3)=9, a(n)=2*a(n-1)-2*a(n-3)+a(n-4). - Harvey P. Dale, Apr 26 2014 MATHEMATICA Flatten[Table[{18 n^2 - 36 n + 9, 18 n^2 - 18 n + 9}, {n, 0, 23}]] (* Bruno Berselli, Oct 01 2012 *) Flatten[Table[18n^2+9-{36n, 18n}, {n, 0, 50}]] (* or *) LinearRecurrence[ {2, 0, -2, 1}, {9, 9, -9, 9}, 100] (* Harvey P. Dale, Apr 26 2014 *) PROG (MAGMA) &cat[[18*k^2-36*k+9, 18*k^2-18*k+9]: k in [0..23]]; // Bruno Berselli, Oct 01 2012 (PARI) vector(47, n, k=(n-1)\2; if(n%2, 18*k^2-36*k+9, 18*k^2-18*k+9)) \\ Bruno Berselli, Oct 01 2012 CROSSREFS Cf. A178218, A214345, A214393, A214405, A216844, A216865, A216875, A216876. Sequence in context: A290624 A290238 A286833 * A251558 A251559 A068395 Adjacent sequences:  A216849 A216850 A216851 * A216853 A216854 A216855 KEYWORD sign,easy AUTHOR Eddie Gutierrez, Sep 17 2012 EXTENSIONS Definition rewritten by Bruno Berselli, Oct 25 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 17 16:08 EST 2019. Contains 329241 sequences. (Running on oeis4.)