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A006060
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Triangular star numbers.
(Formerly M5425)
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2
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1, 253, 49141, 9533161, 1849384153, 358770992581, 69599723176621, 13501987525271953, 2619315980179582321, 508133798167313698381, 98575337528478677903653, 19123107346726696199610361
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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).
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LINKS
| B. Berselli, Table of n, a(n) for n = 1..400. [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Jul 07 2010]
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Eric Weisstein's World of Mathematics, Star Number
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FORMULA
| G.f.: [1+58x+x^2]/[(x-1)(1-194x+x^2)]. - Ralf Stephan, Apr 23 2004
Contribution from Bruno Berselli (berselli.bruno(AT)yahoo.it), 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)
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MAPLE
| A006060:=-(1+58*z+z**2)/(z-1)/(z**2-194*z+1); [Conjectured (correctly) by S. 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); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 14 2008]
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CROSSREFS
| Cf. A000567, A003154, A006061, A051673.
Sequence in context: A123013 A183449 A176087 * A077695 A145628 A144855
Adjacent sequences: A006057 A006058 A006059 * A006061 A006062 A006063
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Extended by Eric Weisstein (eric(AT)weisstein.com), Mar 01, 2002
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