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A163608
a(n) = ((5 + 2*sqrt(2))*(2 + sqrt(2))^n + (5 - 2*sqrt(2))*(2 - sqrt(2))^n)/2.
4
5, 14, 46, 156, 532, 1816, 6200, 21168, 72272, 246752, 842464, 2876352, 9820480, 33529216, 114475904, 390845184, 1334428928, 4556025344, 15555243520, 53108923392, 181325206528, 619082979328, 2113681504256, 7216560058368
OFFSET
0,1
COMMENTS
Binomial transform of A163607. Inverse binomial transform of A163609.
FORMULA
a(n) = 4*a(n-1) - 2*a(n-2) for n > 1; a(0) = 5, a(1) = 14.
G.f.: (5-6*x)/(1-4*x+2*x^2).
a(n) = 5*A007070(n) - 6*A007070(n-1). - R. J. Mathar, Nov 08 2013
E.g.f.: exp(2*x)*( 5*cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Jul 29 2017
MATHEMATICA
LinearRecurrence[{4, -2}, {5, 14}, 30] (* Harvey P. Dale, Jan 31 2017 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+2*r)*(2+r)^n+(5-2*r)*(2-r)^n)/2: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 06 2009
(PARI) x='x+O('x^50); Vec((5-6*x)/(1-4*x+2*x^2)) \\ G. C. Greubel, Jul 29 2017
CROSSREFS
Sequence in context: A336006 A098730 A244236 * A081496 A152051 A220563
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Aug 06 2009
STATUS
approved