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A300297
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Denominators of (1/8)*n*(5 + 3*n)/((1 + 3*n)*(4 + 3*n)), n >= 0.
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1
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1, 28, 280, 520, 416, 608, 1672, 2200, 700, 217, 4216, 5032, 2960, 3440, 7912, 9016, 1274, 2860, 12760, 14152, 7808, 8576, 18760, 20440, 5548, 3002, 25912, 27880, 14960, 16016, 34216, 36472, 2425, 10300, 43672, 46216, 24416, 25760
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OFFSET
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0,2
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COMMENTS
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The numerators are given in A300296, where details and the Jolley reference are given.
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LINKS
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FORMULA
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a(n) = denominator(r(n)), with r(n) = n*(5 + 3*n)/(8*(1 + 3*n)*(4 + 3*n)).
a(n) = (1 + 3*n)*(4 + 3*n)/4 if n == 0 or 9 (mod 32), a(n) = (1 + 3*n)*(4 + 3*n)/2 if n == 16 or 25 (mod 32), a(n) = (1 + 3*n)*(4 + 3*n) if n == 1 or 8 or 17 or 24 (mod 32), and for other n one has a(n) = 2*(1 + 3*n)*(4 + 3*n) if n == 0 or 1 (mod 4) and a(n) = 4*(1 + 3*n)*(4 + 3*n) if n == 2 or 3 (mod 4).
G.f.: G(x) = (1/24)*(1 - hypergeometric([1, 2], [7/3], -x/(1-x)))/(1-x).
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EXAMPLE
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For the first rationals r(n) see A300296.
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PROG
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(PARI) a(n) = denominator((1/8)*n*(5 + 3*n)/((1 + 3*n)*(4 + 3*n))); \\ Altug Alkan, Mar 18 2018
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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STATUS
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approved
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