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A139482
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Binomial transform of [1, 1, 2, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, ...].
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2
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1, 2, 5, 11, 20, 32, 47, 65, 86, 110, 137, 167, 200, 236, 275, 317, 362, 410, 461, 515, 572, 632, 695, 761, 830, 902, 977, 1055, 1136, 1220, 1307, 1397, 1490, 1586, 1685, 1787, 1892, 2000, 2111, 2225
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OFFSET
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1,2
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COMMENTS
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A007318 * [1, 1, 2, 1, -1, 1, -1, 1, ...].
The quadratic expression for a(n) follows at once by taking into account that the alternate row sums in the Pascal triangle are equal to zero (starting with the second row). - Emeric Deutsch, May 03 2008
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=1, a(2)=2, a(3)=5, a(4)=11. - Harvey P. Dale, May 02 2015
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EXAMPLE
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a(4) = 11 = (1, 3, 3, 1) dot (1, 1, 2, 1) = (1 + 3 + 6 + 1).
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MAPLE
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1, 2, 5, 11}, 40] (* Harvey P. Dale, May 02 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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