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102, 404, 906, 1608, 2510, 3612, 4914, 6416, 8118, 10020, 12122, 14424, 16926, 19628, 22530, 25632, 28934, 32436, 36138, 40040, 44142, 48444, 52946, 57648, 62550, 67652, 72954, 78456, 84158, 90060, 96162, 102464, 108966, 115668, 122570
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (100*n+1)^2-(100*n^2+2*n)*(10)^2 = 1 can be written as A158128(n)^2-a(n)*10^2 = 1. - Vincenzo Librandi, Feb 11 2012
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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*(10^2*t+2)).
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.: x*(102+98*x)/(1-x)^3. - Vincenzo Librandi, Feb 11 2012
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Feb 11 2012
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MATHEMATICA
| Table[100n^2 +2n, {n, 45}] (* From Harvey P. Dale, Mar 15 2011 *)
LinearRecurrence[{3, -3, 1}, {102, 404, 906}, 50] (* Vincenzo Librandi, Feb 11 2012 *)
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PROG
| (MAGMA) I:=[102, 404, 906]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 11 2012
(PARI) for(n=1, 50, print1(100*n^2 + 2*n", ")); \\ Vincenzo Librandi, Feb 11 2012
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CROSSREFS
| Cf. A158128.
Sequence in context: A127655 A206659 A206652 * A151964 A088805 A206171
Adjacent sequences: A158124 A158125 A158126 * A158128 A158129 A158130
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009
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