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 A162274 a(n) = ((2+sqrt(3))*(4+sqrt(3))^n + (2-sqrt(3))*(4-sqrt(3))^n)/2. 2
 2, 11, 62, 353, 2018, 11555, 66206, 379433, 2174786, 12465659, 71453054, 409570865, 2347677218, 13456996499, 77136168158, 442148390777, 2534416940162, 14527406441195, 83271831307454, 477318366724097 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Binomial transform of A162273, inverse binomial transform of A162275. LINKS Index entries for linear recurrences with constant coefficients, signature (8, -13). FORMULA a(n) = 8*a(n-1) - 13*a(n-2) for n > 1; a(0) = 2, a(1) = 11. G.f.: (2-5*x)/(1-8*x+13*x^2). MAPLE a := proc (n) options operator, arrow; expand((1/2)*(2+sqrt(3))*(4+sqrt(3))^n+(1/2)*(2-sqrt(3))*(4-sqrt(3))^n) end proc: seq(a(n), n = 0 .. 20); # Emeric Deutsch, Jul 09 2009 PROG (MAGMA) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-3); S:=[ ((2+r)*(4+r)^n+(2-r)*(4-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 05 2009 CROSSREFS Cf. A162273, A162275. Sequence in context: A308729 A034726 A256933 * A183160 A020078 A002629 Adjacent sequences:  A162271 A162272 A162273 * A162275 A162276 A162277 KEYWORD nonn AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Jun 29 2009 EXTENSIONS Edited and extended beyond a(5) by Klaus Brockhaus, Jul 05 2009 STATUS approved

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Last modified February 23 00:28 EST 2020. Contains 332157 sequences. (Running on oeis4.)