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 A161727 a(n) = ((2+sqrt(3))*(4+sqrt(3))^n-(2-sqrt(3))*(4-sqrt(3))^n)/sqrt(12). 1
 1, 6, 35, 202, 1161, 6662, 38203, 219018, 1255505, 7196806, 41252883, 236464586, 1355429209, 7769394054, 44534572715, 255274459018, 1463246226849, 8387401847558, 48077013831427, 275579886633162, 1579637913256745 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Fourth binomial transform of A038754, binomial transform of A140766. LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (8,-13). FORMULA a(n) = 8*a(n-1)-13(n-2) for n > 1; a(0) = 1, a(1) = 6. G.f.: (1-2*x)/(1-8*x+13*x^2). - Klaus Brockhaus, Jun 19 2009 MAPLE seq(expand(((2+sqrt(3))*(4+sqrt(3))^n-(2-sqrt(3))*(4-sqrt(3))^n)/sqrt(12)), n = 0 .. 20) # Emeric Deutsch, Jun 20 2009 MATHEMATICA LinearRecurrence[{8, -13}, {1, 6}, 30] (* Harvey P. Dale, Jun 01 2016 *) PROG (PARI) F=nfinit(x^2-3); for(n=0, 20, print1(nfeltdiv(F, ((2+x)*(4+x)^n-(2-x)*(4-x)^n), (2*x))[1], ", ")) \\ Klaus Brockhaus, Jun 19 2009 CROSSREFS Cf. A038754, A140766. Sequence in context: A081105 A079027 A289784 * A121838 A242629 A001109 Adjacent sequences:  A161724 A161725 A161726 * A161728 A161729 A161730 KEYWORD nonn,easy AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009 EXTENSIONS Extended beyond a(6) by Klaus Brockhaus and Emeric Deutsch, Jun 19 2009 Edited by Klaus Brockhaus, Jul 05 2009 STATUS approved

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Last modified September 20 04:38 EDT 2020. Contains 337264 sequences. (Running on oeis4.)