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A157786
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27225n^2 - 15248n + 2135.
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3
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14112, 80539, 201416, 376743, 606520, 890747, 1229424, 1622551, 2070128, 2572155, 3128632, 3739559, 4404936, 5124763, 5899040, 6727767, 7610944, 8548571, 9540648, 10587175, 11688152, 12843579, 14053456, 15317783, 16636560, 18009787, 19437464, 20919591
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (1482401250*n^2-830253600*n +116250751)^2-(27225*n^2-15248*n +2135) *(8984250*n -2515920)^2=1 can be written as A157788(n)^2-a(n)*A157787(n)^2=1.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Vincenzo Librandi, X^2-AY^2=1
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f: x*(-14112-38203*x-2135*x^2)/(x-1)^3.
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MATHEMATICA
| Table[27225*n^2-15248*n+2135, {n, 50}]
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PROG
| (MAGMA) I:=[14112, 80539, 201416]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..30]];
(PARI) a(n) = 27225*n^2-15248*n+2135.
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CROSSREFS
| Cf. A157787, A157788.
Sequence in context: A066939 A140708 A066698 * A186834 A035918 A206845
Adjacent sequences: A157783 A157784 A157785 * A157787 A157788 A157789
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 06 2009
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EXTENSIONS
| Additional terms provided and Mathematica program provided by Harvey P. Dale, Nov 26 2010
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