|
| |
|
|
A048694
|
|
Generalized Pellian with second term equal to 7.
|
|
6
|
|
|
|
1, 7, 15, 37, 89, 215, 519, 1253, 3025, 7303, 17631, 42565, 102761, 248087, 598935, 1445957, 3490849, 8427655, 20346159, 49119973, 118586105, 286292183, 691170471, 1668633125, 4028436721, 9725506567
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Pisano period lengths: 1, 1, 8, 4, 12, 8, 6, 4, 24, 12, 24, 8, 28, 6, 24, 8, 16, 24, 40, 12, ... . - R. J. Mathar, Aug 10 2012
|
|
|
LINKS
|
Table of n, a(n) for n=0..25.
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2,1)
|
|
|
FORMULA
|
a(n) = ((6+sqrt(2))(1+sqrt(2))^n - (6-sqrt(2))(1-sqrt(2))^n)/2*sqrt(2).
a(n) = 2*a(n-1) + a(n-2); a(0)=1, a(1)=7.
G.f.: (1+5*x)/(1 - 2*x - x^2). - Philippe Deléham, Nov 03 2008
a(n) = ((1+sqrt(18))(1+sqrt(2))^n+(1-sqrt(18))(1-sqrt(2))^n)/2 offset 0. a(n) = first binomial transform of 1,6,2,12,4,24. - Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009
|
|
|
MAPLE
|
with(combinat): a:=n->5*fibonacci(n, 2)+fibonacci(n+1, 2): seq(a(n), n=0..26); # Zerinvary Lajos, Apr 04 2008
|
|
|
MATHEMATICA
|
a[n_]:=(MatrixPower[{{1, 2}, {1, 1}}, n].{{6}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
LinearRecurrence[{2, 1}, {1, 7}, 40] (* Harvey P. Dale, Jul 22 2011 *)
|
|
|
PROG
|
(Maxima)
a[0]:1$
a[1]:7$
a[n]:=2*a[n-1]+a[n-2]$
A048694(n):=a[n]$
makelist(A048694(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */
|
|
|
CROSSREFS
|
Cf. A001333, A000129, A048654, A048655.
Sequence in context: A247606 A146837 A146044 * A041094 A042287 A309732
Adjacent sequences: A048691 A048692 A048693 * A048695 A048696 A048697
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
Barry E. Williams
|
|
|
STATUS
|
approved
|
| |
|
|
