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A163604
a(n) = ((3+2*sqrt(2))*(4+sqrt(2))^n + (3-2*sqrt(2))*(4-sqrt(2))^n)/2.
4
3, 16, 86, 464, 2508, 13568, 73432, 397504, 2151984, 11650816, 63078752, 341518592, 1849046208, 10011109376, 54202228096, 293462293504, 1588867154688, 8602465128448, 46575580861952, 252170135097344, 1365302948711424, 7392041698328576, 40022092304668672
OFFSET
0,1
COMMENTS
Binomial transform of A163606. Inverse binomial transform of A163605.
FORMULA
a(n) = 8*a(n-1)-14*a(n-2) for n > 1; a(0) = 3, a(1) = 16.
G.f.: (3-8*x)/(1-8*x+14*x^2).
E.g.f.: exp(4*x)*( 3*cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Jul 29 2017
MATHEMATICA
LinearRecurrence[{8, -14}, {3, 16}, 50] (* G. C. Greubel, Jul 29 2017 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+2*r)*(4+r)^n+(3-2*r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 07 2009
(PARI) x='x+O('x^50); Vec((3-8*x)/(1-8*x+14*x^2)) \\ G. C. Greubel, Jul 29 2017
CROSSREFS
Sequence in context: A056360 A278681 A224869 * A151329 A356402 A347930
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus and R. J. Mathar, Aug 07 2009
STATUS
approved