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A287733
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First differences of A069497.
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1
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6, 30, 30, 12, 42, 90, 66, 24, 78, 150, 102, 36, 114, 210, 138, 48, 150, 270, 174, 60, 186, 330, 210, 72, 222, 390, 246, 84, 258, 450, 282, 96, 294, 510, 318, 108, 330, 570, 354, 120, 366, 630, 390, 132, 402, 690, 426, 144, 438, 750, 462, 156, 474, 810, 498, 168, 510, 870, 534
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OFFSET
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1,1
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COMMENTS
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First differences of the subsequence of triangular numbers that are divisible by 6.
By definition, these numbers are themselves divisible by 6.
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LINKS
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FORMULA
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G.f.: 6*(x^2+4*x+1)*(x^2-x+1)/((x-1)^2*(x^2+1)^2). - Robert Israel, May 30 2017
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EXAMPLE
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The first triangular number divisible by 6 is 6, and the second triangular number divisible by 6 is 36. Therefore a(2) = 36 - 6 = 30. (The zeroeth triangular number divisible by 6 is taken to be 0.)
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MAPLE
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S:= [seq(seq((12*i+j)*(12*i+j+1)/2, j=[0, 3, 8, 11]), i=0..50)]:
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MATHEMATICA
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Differences@ Select[Array[# (# + 1)/2 &, 180, 0], Mod[#, 6] == 0 &] (* Robert G. Wilson v, May 30 2017 *)
Differences[Select[Accumulate[Range[0, 209]], Divisible[#, 6] &]] (* Alonso del Arte, May 31 2017 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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