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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Fourth binomial transform of A162255. LINKS Muniru A Asiru, Table of n, a(n) for n = 0..280 Index entries for linear recurrences with constant coefficients, signature (8, -14). 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:=PolynomialRing(Integers()); N:=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 Adjacent sequences:  A161936 A161937 A161938 * A161940 A161941 A161942 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

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Last modified January 25 03:49 EST 2020. Contains 331241 sequences. (Running on oeis4.)