|
| |
|
|
A216853
|
|
18k^2-12k-7 interleaved with 18k^2+6k+5 for k>=0.
|
|
0
|
|
|
|
-7, 5, -1, 29, 41, 89, 119, 185, 233, 317, 383, 485, 569, 689, 791, 929, 1049, 1205, 1343, 1517, 1673, 1865, 2039, 2249, 2441, 2669, 2879, 3125, 3353, 3617, 3863, 4145, 4409, 4709, 4991, 5309, 5609, 5945, 6263, 6617, 6953, 7325, 7679, 8069, 8441, 8849
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
The sequence (the third in the family) 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..45.
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
|
G.f.: -(7-19*x+11*x^2-17*x^3)/((1+x)*(1-x)^3). - Bruno Berselli, Oct 05 2012
a(n) = (6*n*(3*n-4)-27*(-1)^n-1)/4. - Bruno Berselli, Oct 05 2012
|
|
|
MATHEMATICA
|
Flatten[Table[{18 n^2 - 12 n - 7, 18 n^2 + 6 n + 5}, {n, 0, 22}]] (* Bruno Berselli, Oct 05 2012 *)
|
|
|
PROG
|
(MAGMA) &cat[[18*k^2-12*k-7, 18*k^2+6*k+5]: k in [0..22]]; // Bruno Berselli, Oct 05 2012
(PARI) vector(46, n, k=(n-1)\2; if(n%2, 18*k^2-12*k-7, 18*k^2+6*k+5)) \\ Bruno Berselli, Oct 05 2012
|
|
|
CROSSREFS
|
Cf. A178218, A214345, A214393, A214405, A216876.
Sequence in context: A323811 A316334 A196486 * A084911 A272169 A073742
Adjacent sequences: A216850 A216851 A216852 * A216854 A216855 A216856
|
|
|
KEYWORD
|
sign,easy
|
|
|
AUTHOR
|
Eddie Gutierrez, Sep 17 2012
|
|
|
EXTENSIONS
|
Definition rewritten by Bruno Berselli, Oct 25 2012
|
|
|
STATUS
|
approved
|
| |
|
|
