PROG
(MAGMAMagma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+r)*(4+r)^n+(3-r)*(4-r)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 01 2009
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Revision History for A161939
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
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NAME
a(n) = ((3+sqrt(2))*(4+sqrt(2))^n + (3-sqrt(2))*(4-sqrt(2))^n)/2.
PROG
(PARI) x='x+O('x^30); Vec((3-10*x)/(1-8*x+14*x^2)) \\ G. C. Greubel, Aug 17 2018
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FORMULA
From Emeric Deutsch, Jun 28 2009: (Start)
G.f.=(3-10x)/(1-8x+14x^2).
Recursive relation: a(n) = 8a(n-1) - 14a(n-2); a(0)=3, a(1)=14.
(End)
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LINKS
Muniru A Asiru, <a href="/A161939/b161939.txt">Table of n, a(n) for n = 0..280</a>
PROG
(GAP) a := [3, 14];; for n in [3..10^2] do a[n] := 8*a[n-1] - 14*a[n-2]; od; a; # Muniru A Asiru, Feb 02 2018
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