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A162558
a(n) = ((3+sqrt(3))*(5+sqrt(3))^n + (3-sqrt(3))*(5-sqrt(3))^n)/6.
2
1, 6, 38, 248, 1644, 10984, 73672, 495072, 3329936, 22407776, 150819168, 1015220608, 6834184384, 46006990464, 309717848192, 2085024691712, 14036454256896, 94493999351296, 636137999861248, 4282512012883968
OFFSET
0,2
COMMENTS
Fifth binomial transform of A108411. Binomial transform of A162557. Inverse binomial transform of A162757.
2nd binomial transform of A086405. - R. J. Mathar, Jul 17 2009
FORMULA
a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0) = 1, a(1) = 6.
G.f.: (1-4*x)/(1-10*x+22*x^2).
From R. J. Mathar, Jul 17 2009: (Start)
a(n) = 10*a(n-2) - 22*a(n-2).
G.f.: (1-4*x)/(1-10*x+22*x^2). (End)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((3+r)*(5+r)^n+(3-r)*(5-r)^n)/6: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 13 2009
CROSSREFS
Cf. A108411 (powers of 3 repeated), A162557, A162757.
Sequence in context: A377114 A135030 A217633 * A215466 A147957 A098410
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Jul 13 2009
More terms from R. J. Mathar, Jul 17 2009
STATUS
approved