|
| |
|
|
A164535
|
|
a(n) = 8*a(n-1)-14*a(n-2) for n > 1; a(0) = 3, a(1) = 20.
|
|
3
| |
|
|
3, 20, 118, 664, 3660, 19984, 108632, 589280, 3193392, 17297216, 93670240, 507200896, 2746223808, 14868977920, 80504690048, 435871829504, 2359908975360, 12777066189824, 69177803863552, 374543504250880
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| Binomial transform of A164305. Fourth binomial transform of A164654. Inverse binomial transform of A164536.
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..158
|
|
|
FORMULA
| a(n) = 8*a(n-1)-14*a(n-2) for n > 1; a(0) = 3, a(1) = 20.
G.f.: (3-4*x)/(1-8*x+14*x^2).
a(n) = ((3+4*sqrt(2))*(4+sqrt(2))^n+(3-4*sqrt(2))*(4-sqrt(2))^n)/2.
|
|
|
MATHEMATICA
| CoefficientList[Series[(3-4x)/(1-8x+14x^2), {x, 0, 25}], x] (* From Harvey P. Dale, Feb 23 2011 *)
|
|
|
PROG
| (MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+4*r)*(4+r)^n+(3-4*r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 20 2009]
|
|
|
CROSSREFS
| Cf. A164305, A164654, A164536.
Sequence in context: A178711 A108911 A005096 * A001652 A128910 A037788
Adjacent sequences: A164532 A164533 A164534 * A164536 A164537 A164538
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009
|
|
|
EXTENSIONS
| Edited and extended beyond a(5) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 20 2009
|
| |
|
|
