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A081065
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Numbers n such that n^2 = (1/3)*(n+floor(sqrt(3)*n*floor(sqrt(3)*n))).
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1
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2, 24, 330, 4592, 63954, 890760, 12406682, 172802784, 2406832290, 33522849272, 466913057514, 6503259955920, 90578726325362, 1261598908599144, 17571805994062650, 244743685008277952, 3408839784121828674
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n)/2 gives indices of pentagonal numbers which are also triangular. a(n) itself gives x-values solving the Diophantine equation 2*x^2 + (x-1)^2 = y^2.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (15,-15,1).
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FORMULA
| a(n) = 15*a(n-1) - 15*a(n-2) + a(n-3).
a(n) = 14*a(n-1) - a(n-2) - 4. [Sture Sjöstedt, May 02 2011]
G.f.: 2*(1-3*x)/((1-x)*(1-14*x+x^2)). - Bruno Berselli, Nov 11 2011
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CROSSREFS
| Cf. A046090, A046174, A046175.
Sequence in context: A001864 A099045 A181174 * A043699 A134805 A119702
Adjacent sequences: A081062 A081063 A081064 * A081066 A081067 A081068
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KEYWORD
| nonn,easy
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 15 2003
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