|
| |
|
|
A056236
|
|
(2+sqrt(2))^n+(2-sqrt(2))^n.
|
|
4
| |
|
|
2, 4, 12, 40, 136, 464, 1584, 5408, 18464, 63040, 215232, 734848, 2508928, 8566016, 29246208, 99852800, 340918784, 1163969536, 3974040576, 13568223232, 46324811776, 158162800640, 540001579008, 1843680714752, 6294719700992
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
FORMULA
| a(n) = 4*a(n-1)-2*a(n-2) = a(n-2)-a(n-1)+2*A020727(n-1) = 2*A006012(n) = 4*A007052(n-1). For n>2, a(n) = floor[(2+sqrt(2))*a(n-1)].
G.f.: (2-4x)/(1-4x+2x^2).
a(n)=2^(2*n)*[cos(Pi/8)^(2*n)+cos(3*Pi/8)^2*n]; also, a(n)=3*a(n-1)+Sum{k=1..n-2} a(k), for n>1, with a(0)=2, a(1)=4. - L. Edson Jeffery, April 8, 2011.
|
|
|
PROG
| (PARI) a(n)=2*real((2+quadgen(8))^n)
sage: [lucas_number2(n, 4, 2) for n in range(37)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008
|
|
|
CROSSREFS
| Sequence in context: A099214 A126946 A113179 * A028329 A204678 A025227
Adjacent sequences: A056233 A056234 A056235 * A056237 A056238 A056239
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Aug 11 2000
|
|
|
EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 25 2000
|
| |
|
|
