|
| |
|
|
A048694
|
|
Generalized Pellian with second term equal to 7.
|
|
5
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
|
|
|
FORMULA
| 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). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
a(n)=((1+sqrt18)(1+sqrt2)^n+(1-sqrt18)(1-sqrt2)^n)/2 offset 0. a(n)=first binomial transform of 1,6,2,12,4,24 [From Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009]
|
|
|
EXAMPLE
| a(n)=[ (6+sqrt(2))(1+sqrt(2))^n - (6-sqrt(2))(1-sqrt(2))^n ]/2*sqrt(2)
|
|
|
MAPLE
| with(combinat): a:=n->5*fibonacci(n-1, 2)+fibonacci(n, 2): seq(a(n), n=1..26); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008
|
|
|
MATHEMATICA
| a[n_]:=(MatrixPower[{{1, 2}, {1, 1}}, n].{{6}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 20 2010]
LinearRecurrence[{2, 1}, {1, 7}, 40] (* From Harvey P. Dale, Jul 22 2011 *)
|
|
|
CROSSREFS
| Cf. A001333, A000129, A048654, A048655.
Sequence in context: A159792 A146837 A146044 * A041094 A042287 A145978
Adjacent sequences: A048691 A048692 A048693 * A048695 A048696 A048697
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Barry E. Williams
|
| |
|
|
