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627, 2504, 5631, 10008, 15635, 22512, 30639, 40016, 50643, 62520, 75647, 90024, 105651, 122528, 140655, 160032, 180659, 202536, 225663, 250040, 275667, 302544, 330671, 360048, 390675, 422552, 455679, 490056, 525683, 562560, 600687, 640064
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (625*n+1)^2-(625*n^2+2*n)*(25)^2=1 can be written as A158383(n)^2-a(n)*(25)^2=1.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1
E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(25^2*t+2)).
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*(-627-631*x)/(x-1)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {627, 2504, 5631}, 50]
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PROG
| (MAGMA) I:=[627, 2504, 5631]; [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) = 625*n^2 + 2*n.
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CROSSREFS
| Cf. A158383.
Sequence in context: A031523 A129974 A031703 * A188362 A098260 A098261
Adjacent sequences: A158379 A158380 A158381 * A158383 A158384 A158385
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 17 2009
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