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A140230
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Binomial transform of [1, 2, -3, -4, 5, 6, -7, -8, 9, 10,...].
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2
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1, 3, 2, -6, -20, -28, -8, 56, 144, 176, 32, -352, -832, -960, -128, 1920, 4352, 4864, 512, -9728, -21504, -23552, -2048, 47104, 102400, 110592, 8192, -221184, -475136, -507904, -32768, 1015808, 2162688, 2293760, 131072, -4587520, -9699328
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..206
Index to sequences with linear recurrences with constant coefficients, signature (4,-8,8,-4).
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FORMULA
| A007318 * [1, 2, -3, -4, 5, 6, -7, -8, 9, 10,...]; i.e. (+) signs when n == 1 or 2 MOD 4; (-) otherwise.
a(1+4*n) + a(2+4*n) + a(3+4*n) + a(4+4*n) = 0. - Paul Curtz, Apr 22 2011
a(n) = +4*a(n-1) -8*a(n-2) +8*a(n-3) -4*a(n-4) [Joerg Arndt, Apr 25 2011]
G.f. x*(x-1)*(2*x^2-1) / ( (1-2*x+2*x^2)^2 ). - R. J. Mathar, Jun 02 2011
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EXAMPLE
| a(4) = -6 = (1, 3, 3, 1) dot (1, 2, -3, -4) = (1 + 6 - 9 - 4).
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PROG
| (Pari) Vec((2*x^3-2*x^2-x+1)/(4*x^4-8*x^3+8*x^2-4*x+1)+O(x^66)) /* Joerg Arndt, Apr 25 2011 */
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CROSSREFS
| Sequence in context: A007812 A082561 A110768 * A025240 A137602 A018864
Adjacent sequences: A140227 A140228 A140229 * A140231 A140232 A140233
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KEYWORD
| sign,easy
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 13 2008
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