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(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
KEYWORD
sign,easy
AUTHOR
Eddie Gutierrez, Sep 17 2012
EXTENSIONS
Definition rewritten by Bruno Berselli, Oct 25 2012
STATUS
approved