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A140164
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Binomial transform of [1, 1, 1, 1, -1, -1, 5, -11, 19, -29, 41,...].
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1
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1, 2, 4, 8, 14, 20, 26, 32, 38, 44, 50, 56, 62, 68, 74, 80, 86, 92, 98, 104, 110, 116, 122, 128, 134, 140, 146, 152, 158, 164, 170, 176, 182, 188, 194, 200, 206, 212, 218, 224, 230, 236, 242, 248, 254, 260, 266, 272, 278, 284, 290, 296, 302, 308, 314, 320, 326
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Sum of antidiagonal terms of the following arithmetic array:
1, 1, 1, 1, 1,...
1, 2, 3, 4, 5,...
1, 3, 5, 7, 9,...
1, 4, 7, 10, 13,...
...
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FORMULA
| Binomial transform of [1, 1, 1, 1, -1, -1, 5, -11, 19, -29, 41, -55,...]; where A028387 = (1, 5, 11, 19, 29, 41,...), such that A028387(n) = (2*T(n) - 1).
G.f.: 2*x^3*(4-x)/(x-1)^2. a(n) = A016933(n-2), n>2. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 03 2010]
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EXAMPLE
| a(4) = 8 = (1, 3, 3, 1) dot (1, 1, 1, 1) = (1 + 3 + 3 + 1).
a(5) = 14 = (4 + 5 + 4 + 1).
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MAPLE
| Contribution from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 03 2010: (Start)
A028387 := proc(n) option remember; if n <= 2 then op(n+1, [1, 5, 11]) ; else 3*procname(n-1)-3*procname(n-2)+procname(n-3) ; end if; end proc:
read("transforms") ; L := [1, 1, 1, 1, -1, seq((-1)^(n+1)*A028387(n), n=0..100)]; BINOMIAL(L) ; (End)
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CROSSREFS
| Cf. A028387.
Sequence in context: A084621 A002132 A169926 * A160730 A190402 A175300
Adjacent sequences: A140161 A140162 A140163 * A140165 A140166 A140167
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 10 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 03 2010
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