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A162395
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(-1)^(n+1) * n^2.
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4
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1, -4, 9, -16, 25, -36, 49, -64, 81, -100, 121, -144, 169, -196, 225, -256, 289, -324, 361, -400, 441, -484, 529, -576, 625, -676, 729, -784, 841, -900, 961, -1024, 1089, -1156, 1225, -1296, 1369, -1444, 1521, -1600, 1681, -1764, 1849, -1936, 2025, -2116, 2209, -2304, 2401, -2500
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OFFSET
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1,2
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COMMENTS
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This sequence is the denominator of ((pi)^2)/12 = 1/1-1/4+1/9-1/16+1/25-1/36+... - Mohammad K. Azarian, Dec 29 2011
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
M. Somos, Rational Function Multiplicative Coefficients
Index to sequences with linear recurrences with constant coefficients, signature (-3,-3,-1).
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FORMULA
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Euler transform of length 2 sequence [ -4, 3].
a(n) is multiplicative with a(2^e) = -(4^e) if e>0, a(p^e) = (p^2)^e if p>2.
G.f.: x * (1 - x) / (1 + x)^3. E.g.f.: exp(-x) * (x - x^2).
a(-n) = -(-1)^n A000290(n) = a(n).
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EXAMPLE
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x - 4*x^2 + 9*x^3 - 16*x^4 + 25*x^5 - 36*x^6 + 49*x^7 - 64*x^8 + 81*x^9 + ...
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MATHEMATICA
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Table[(-1)^(n+1) * n^2, {n, 60}] (* Vincenzo Librandi, Feb 15 2013 *)
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PROG
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(PARI) {a(n) = -(-1)^n * n^2}
(MAGMA) [(-1)^(n+1) * n^2: n in [1..60]]; // Vincenzo Librandi, Feb 15 2013
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CROSSREFS
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Cf. A000290.
Sequence in context: A174452 A174902 A000290 * A221222 A144913 A018885
Adjacent sequences: A162392 A162393 A162394 * A162396 A162397 A162398
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KEYWORD
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sign,mult,easy
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AUTHOR
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Michael Somos, Jul 02 2009
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STATUS
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approved
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