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A006062
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Star-hex numbers.
(Formerly M5265)
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7
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1, 37, 1261, 42841, 1455337, 49438621, 1679457781, 57052125937, 1938092824081, 65838103892821, 2236557439531837, 75977114840189641, 2580985347126915961, 87677524687474953037, 2978454854027021487301, 101179787512231255615201
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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REFERENCES
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M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 22.
H. J. Hindin, Stars, hexes, triangular numbers and Pythagorean triples, J. Rec. Math., 16 (1983/1984), 191-193.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=1..16.
H. J. Hindin, Stars, hexes, triangular numbers and Pythagorean triples, J. Rec. Math., 16 (1983/1984), 191-193. (Annotated scanned copy)
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
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FORMULA
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a(n) = 34*a(n-1) - a(n-2) + 4.
G.f.: -x*(x + 1)^2/(x - 1)/(x^2 - 34*x + 1) [from Simon Plouffe, see Maple code].
From Charlie Marion, Aug 03 2005: (Start)
a(n) = A001109(n-1)^2 + A001109(n)^2; e.g., 1261 = 6^2 + 35^2.
a(n) = A001652(n-1)*A046090(n-1) + A001653(n-1)^2; e.g., 1261 = 20*21 + 29^2. (End)
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MAPLE
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A006062:=-(z+1)**2/(z-1)/(z**2-34*z+1); [Simon Plouffe in his 1992 dissertation for offset zero.]
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CROSSREFS
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Sequence in context: A099201 A218841 A246461 * A219420 A162851 A163220
Adjacent sequences: A006059 A006060 A006061 * A006063 A006064 A006065
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Jul 11 1991
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STATUS
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approved
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