|
| |
| |
|
|
|
5, 29, 69, 125, 197, 285, 389, 509, 645, 797, 965, 1149, 1349, 1565, 1797, 2045, 2309, 2589, 2885, 3197, 3525, 3869, 4229, 4605, 4997, 5405, 5829, 6269, 6725, 7197, 7685, 8189, 8709, 9245, 9797, 10365, 10949, 11549, 12165, 12797, 13445, 14109, 14789
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Sequence found by reading the segment (5, 29) together with the line from 29, in the direction 29, 69,..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 04 2011
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
|
|
|
FORMULA
|
a(n) = 2*(2*n-1)*(2*n+1)-1.
a(0)=5, a(1)=29, a(2)=69, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) -- From Harvey P. Dale, Jul 21 2012
|
|
|
EXAMPLE
|
(1*3 = 3)+2 = 5; (3*5 = 15)+14 = 29; (5*7 = 35)+34 = 69; (7*9 = 63)+62 = 125; ...
|
|
|
MAPLE
|
seq(8*n^2-3, n=1..50); (Emeric Deutsch)
|
|
|
MATHEMATICA
|
8*Range[50]^2-3 (* or *) LinearRecurrence[{3, -3, 1}, {5, 29, 69}, 50] (* Harvey P. Dale, Jul 21 2012 *)
|
|
|
PROG
|
(PARI) a(n)=8*n^2-3 \\ Charles R Greathouse IV, Sep 04 2011
(MAGMA) [8*n^2 - 3: n in [1..50]]; // Vincenzo Librandi, Sep 05 2011
|
|
|
CROSSREFS
|
Sequence in context: A115706 A031394 A103094 * A097812 A176333 A100559
Adjacent sequences: A108925 A108926 A108927 * A108929 A108930 A108931
|
|
|
KEYWORD
|
easy,nonn,changed
|
|
|
AUTHOR
|
Marcel Hetkowski Fabeny (marcelfabeny(AT)yahoo.com.br), Jul 19 2005
|
|
|
EXTENSIONS
|
More terms from Emeric Deutsch, Aug 01 2005
|
|
|
STATUS
|
approved
|
| |
|
|
