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A164536
a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 3, a(1) = 23.
2
3, 23, 161, 1081, 7107, 46207, 298609, 1923329, 12365283, 79416263, 509761121, 3271037161, 20985865827, 134624803567, 863573121649, 5539360734449, 35531425546563, 227908958573303, 1461866798162081, 9376761934434841
OFFSET
0,1
COMMENTS
Binomial transform of A164535. Fifth binomial transform of A164654.
FORMULA
a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 3, a(1) = 23.
G.f.: (3-7*x)/(1-10*x+23*x^2).
a(n) = ((3+4*sqrt(2))*(5+sqrt(2))^n + (3-4*sqrt(2))*(5-sqrt(2))^n)/2.
MATHEMATICA
LinearRecurrence[{10, -23}, {3, 23}, 30] (* or *) CoefficientList[Series[ (3-7*x)/(1-10*x+23*x^2), {x, 0, 30}], x] (* Harvey P. Dale, Dec 18 2011 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+4*r)*(5+r)^n+(3-4*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 20 2009
CROSSREFS
Sequence in context: A006184 A308677 A209011 * A037789 A037670 A037796
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Aug 20 2009
STATUS
approved