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 A161947 a(n) = ((4+sqrt(2))*(5+sqrt(2))^n + (4-sqrt(2))*(5-sqrt(2))^n)/4. 2
 2, 11, 64, 387, 2398, 15079, 95636, 609543, 3895802, 24938531, 159781864, 1024232427, 6567341398, 42116068159, 270111829436, 1732448726703, 11111915190002, 71272831185851, 457154262488464, 2932267507610067 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Fifth binomial transform of A135530. LINKS Muniru A Asiru, Table of n, a(n) for n = 0..252 Index entries for linear recurrences with constant coefficients, signature (10,-23). FORMULA a(n) = 10*a(n-1) - 23*a(n-2) for n>1; a(0) = 2; a(1) = 11. G.f.: (2-9*x)/(1-10*x+23*x^2). MAPLE seq(simplify(((4+sqrt(2))*(5+sqrt(2))^n+(4-sqrt(2))*(5-sqrt(2))^n)*1/4), n = 0 .. 20); # Emeric Deutsch, Jun 28 2009 MATHEMATICA LinearRecurrence[{10, -23}, {2, 11}, 50] (* G. C. Greubel, Aug 17 2018 *) Table[(((4+Sqrt[2])(5+Sqrt[2])^n)+((4-Sqrt[2])(5-Sqrt[2])^n))/4, {n, 0, 20}]//Simplify (* Harvey P. Dale, Mar 07 2020 *) PROG (MAGMA) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((4+r)*(5+r)^n+(4-r)*(5-r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 01 2009 (GAP) a := [2, 11];; for n in [3..10^2] do a[n] := 10*a[n-1] - 23*a[n-2]; od; a; # Muniru A Asiru, Feb 02 2018 (PARI) x='x+O('x^30); Vec((2-9*x)/(1-10*x+23*x^2)) \\ G. C. Greubel, Aug 17 2018 CROSSREFS Cf. A135530. Sequence in context: A126745 A179120 A038725 * A001565 A199412 A074613 Adjacent sequences:  A161944 A161945 A161946 * A161948 A161949 A161950 KEYWORD nonn AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Jun 22 2009 EXTENSIONS Edited and extended beyond a(4) by Klaus Brockhaus, Jul 01 2009 Extended by Emeric Deutsch, Jun 28 2009 STATUS approved

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Last modified November 25 05:43 EST 2020. Contains 338617 sequences. (Running on oeis4.)