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A062781
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Number of arithmetic progressions of four terms and any mean which can be extracted from the set of the first n positive integers.
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3
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0, 0, 0, 1, 2, 3, 5, 7, 9, 12, 15, 18, 22, 26, 30, 35, 40, 45, 51, 57, 63, 70, 77, 84, 92, 100, 108, 117, 126, 135, 145, 155, 165, 176, 187, 198, 210, 222, 234, 247, 260, 273, 287, 301, 315, 330, 345, 360, 376, 392
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OFFSET
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1,5
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COMMENTS
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This sequence seems to be a shifted version of the Somos sequence A058937.
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LINKS
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FORMULA
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a(n) = P(n,4), where P(n,k) = n*floor(n/(k - 1)) - (1/2)(k - 1)(floor(n/(k - 1))*(floor(n/(k - 1)) + 1)); recursion: a(n) = a(n-3) + n - 3; a(1) = a(2) = a(3) = 0.
a(n) = (1/2)*floor((n-1)/3)*(2*n - 3 - 3*floor((n-1)/3)).
G.f.: x^4/((1 - x^3)*(1 - x)^2). (End)
a(n) = floor((n-1)/3) + a(n-1). - Jon Maiga, Nov 25 2018
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MAPLE
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seq(coeff(series(x^4/((1-x^3)*(1-x)^2), x, n+1), x, n), n = 1 .. 50); # Muniru A Asiru, Nov 25 2018
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MATHEMATICA
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RecurrenceTable[{a[0]==0, a[n]==Floor[n/3] + a[n-1]}, a, {n, 49}] (* Jon Maiga, Nov 25 2018 *)
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PROG
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(Sage) [floor(binomial(n, 2)/3) for n in range(0, 50)] # Zerinvary Lajos, Dec 01 2009
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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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STATUS
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approved
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