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A162772
a(n) = ((2+sqrt(5))*(4+sqrt(5))^n + (2-sqrt(5))*(4-sqrt(5))^n)/2.
3
2, 13, 82, 513, 3202, 19973, 124562, 776793, 4844162, 30208573, 188382802, 1174768113, 7325934082, 45685023413, 284894912402, 1776624041673, 11079148296962, 69090321917293, 430851944071762, 2686822011483873
OFFSET
0,1
COMMENTS
Binomial transform of A162771. Fourth binomial transform of A162963. Inverse binomial transform of A162773.
FORMULA
a(n) = 8*a(n-1) - 11*a(n-1) for n > 1; a(0) = 2, a(1) = 13.
G.f.: (2-3*x)/(1-8*x+11*x^2).
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((2+r)*(4+r)^n+(2-r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 19 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jul 13 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Jul 19 2009
STATUS
approved