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A164035
a(n) = ((4+3*sqrt(2))*(5+sqrt(2))^n + (4-3*sqrt(2))*(5-sqrt(2))^n)/4.
3
2, 13, 84, 541, 3478, 22337, 143376, 920009, 5902442, 37864213, 242885964, 1557982741, 9993450238, 64100899337, 411159637896, 2637275694209, 16916085270482, 108503511738013, 695965156159044, 4464070791616141
OFFSET
0,1
COMMENTS
Binomial transform of A164034. Fifth binomial transform of A164090.
FORMULA
a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 2, a(1) = 13.
G.f.: (2-7*x)/(1-10*x+23*x^2).
E.g.f.: (2*cosh(sqrt(2)*x) + (3*sqrt(2)/2)*sinh(sqrt(2)*x))*exp(5*x). - G. C. Greubel, Sep 08 2017
MATHEMATICA
LinearRecurrence[{10, -23}, {2, 13}, 50] (* or *) CoefficientList[Series[(2 - 7*x)/(1 - 10*x + 23*x^2), {x, 0, 50}], x] (* _G. C. Greubel, Sep 08 2017 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((4+3*r)*(5+r)^n+(4-3*r)*(5-r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 09 2009
(PARI) x='x+O('x^50); Vec((2-7*x)/(1-10*x+23*x^2)) \\ G. C. Greubel, Sep 08 2017
CROSSREFS
Sequence in context: A156018 A285795 A134148 * A074619 A162275 A092070
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Aug 09 2009
STATUS
approved