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A161939
a(n) = ((3+sqrt(2))*(4+sqrt(2))^n + (3-sqrt(2))*(4-sqrt(2))^n)/2.
2
3, 14, 70, 364, 1932, 10360, 55832, 301616, 1631280, 8827616, 47783008, 258677440, 1400457408, 7582175104, 41050997120, 222257525504, 1203346244352, 6515164597760, 35274469361152, 190983450520576, 1034025033108480
OFFSET
0,1
COMMENTS
Fourth binomial transform of A162255.
FORMULA
a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 3; a(1) = 14.
G.f.: (3-10*x)/(1-8*x+14*x^2).
MAPLE
seq(simplify(((3+sqrt(2))*(4+sqrt(2))^n+(3-sqrt(2))*(4-sqrt(2))^n)*1/2), n = 0 .. 20); # Emeric Deutsch, Jun 28 2009
MATHEMATICA
LinearRecurrence[{8, -14}, {3, 14}, 30] (* Harvey P. Dale, May 10 2012 *)
PROG
(Magma) 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
(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
(PARI) x='x+O('x^30); Vec((3-10*x)/(1-8*x+14*x^2)) \\ G. C. Greubel, Aug 17 2018
CROSSREFS
Cf. A162255, A161940 (Fifth binomial transform of A162255).
Sequence in context: A028938 A038213 A261207 * A270598 A001579 A327871
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jun 22 2009
EXTENSIONS
Definition corrected by Emeric Deutsch, Jun 28 2009
Edited and extended beyond a(5) by Klaus Brockhaus, Jul 01 2009
Extended by Emeric Deutsch, Jun 28 2009
STATUS
approved