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 A006060 Triangular star numbers. (Formerly M5425) 2
 1, 253, 49141, 9533161, 1849384153, 358770992581, 69599723176621, 13501987525271953, 2619315980179582321, 508133798167313698381, 98575337528478677903653, 19123107346726696199610361 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 20. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS B. Berselli, Table of n, a(n) for n = 1..400. [From Bruno Berselli, Jul 07 2010] Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992. Eric Weisstein's World of Mathematics, Star Number Index entries for linear recurrences with constant coefficients, signature (195, -195, 1). FORMULA G.f.: [1+58x+x^2]/[(x-1)(1-194x+x^2)]. - Ralf Stephan, Apr 23 2004 From Bruno Berselli, Jul 07 2010: (Start) a(n) = 194*a(n-1)-a(n-2)+60 (n>2). a(n) = (3*((7+4*3^(1/2))^(2*n-1)+(7-4*3^(1/2))^(2*n-1))-10)/32 (n>0). (End) MAPLE A006060:=-(1+58*z+z**2)/(z-1)/(z**2-194*z+1); [Conjectured (correctly) by Simon Plouffe in his 1992 dissertation.] a:= n-> (Matrix([[253, 1, 1]]). Matrix([[195, 1, 0], [ -195, 0, 1], [1, 0, 0]])^n)[1, 3]: seq(a(n), n=1..20); # Alois P. Heinz, Aug 14 2008 MATHEMATICA a006060 = {}; Do[ If[Length[a006060] < 2, AppendTo[a006060, 1],   AppendTo[a006060, 194*a006060[[-1]] + 60 - a006060[[-2]]]],  {n,   20}]; TableForm[Transpose[List[Range[Length[a006060]], a006060]]] (* Michael De Vlieger *) LinearRecurrence[{195, -195, 1}, {1, 253, 49141}, 20] (* Harvey P. Dale, Jan 12 2017 *) CROSSREFS Cf. A000567, A003154, A006061, A051673. Sequence in context: A271985 A255182 A176087 * A077695 A253880 A145628 Adjacent sequences:  A006057 A006058 A006059 * A006061 A006062 A006063 KEYWORD nonn AUTHOR EXTENSIONS Extended by Eric W. Weisstein, Mar 01 2002 STATUS approved

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Last modified November 14 19:12 EST 2018. Contains 317214 sequences. (Running on oeis4.)