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99, 398, 897, 1596, 2495, 3594, 4893, 6392, 8091, 9990, 12089, 14388, 16887, 19586, 22485, 25584, 28883, 32382, 36081, 39980, 44079, 48378, 52877, 57576, 62475, 67574, 72873, 78372, 84071, 89970, 96069, 102368, 108867, 115566, 122465, 129564
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (200*n-1)^2-(100*n^2-n)*(20)^2=1 can be written as A157955(n)^2-a(n)*(20)^2=1 (see Barbeau's paper).
Also, the identity (80000*n^2-800*n+1)^2-(100*n^2-n)*(8000*n-40)^2=1 can be written as A157661(n)^2-a(n)*A157660(n)^2=1 (see also the second part of the comment in A157661). - Vincenzo Librandi, Jan 28 2012
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 14 in the first table at p. 85, case d(t) = t*(10^2*t-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*(-99-101*x)/(x-1)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {99, 398, 897}, 50]
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PROG
| (MAGMA) I:=[99, 398, 897]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n)=100*n^2-n \\ Charles R Greathouse IV, Dec 28 2011
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CROSSREFS
| Cf. A157660, A157661, A157995.
Sequence in context: A008882 A156757 A027579 * A154359 A185499 A061366
Adjacent sequences: A157656 A157657 A157658 * A157660 A157661 A157662
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 04 2009
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