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A157078
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32805000n^2 - 55096200n + 23133601.
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3
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842401, 44161201, 153090001, 327628801, 567777601, 873536401, 1244905201, 1681884001, 2184472801, 2752671601, 3386480401, 4085899201, 4850928001, 5681566801, 6577815601, 7539674401, 8567143201, 9660222001, 10818910801, 12043209601
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity(32805000*n^2-55096200*n+23133601)^2-(2025*n^2-649*n+52)*(729000*n-612180)^2=1 can be written as a(n)^2-A156853(n)*A156865(n)^2=1.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
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*(-842401-41633998*x-23133601*x^2)/(x-1)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {842401, 44161201, 153090001}, 40]
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PROG
| (MAGMA) I:=[842401, 44161201, 153090001]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..30]];
(PARI) a(n)=32805000*n^2-55096200*n+23133601 \\ Charles R Greathouse IV, Dec 23 2011
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CROSSREFS
| Cf. A156853, A156865.
Sequence in context: A015390 A043623 A185520 * A160548 A141296 A103913
Adjacent sequences: A157075 A157076 A157077 * A157079 A157080 A157081
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 22 2009
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