A216852 18k^2-36k+9 interleaved with 18k^2-18k+9 for k>=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

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

Table of n, a(n) for n=0..46.

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