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A271999
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Halogen sequence: a(n) = A018227(n)-1.
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2
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1, 11, 17, 35, 53, 85, 117, 167, 217, 289, 361, 459, 557, 685, 813, 975, 1137, 1337, 1537, 1779, 2021, 2309, 2597, 2935, 3273, 3665, 4057, 4507, 4957, 5469, 5981, 6559, 7137, 7785, 8433, 9155, 9877, 10677, 11477, 12359, 13241, 14209, 15177, 16235, 17293
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OFFSET
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1,2
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COMMENTS
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Terms from 11 to 117 are the atomic numbers of the elements in group 17 in the periodic table. The elements in this group are also called halogens.
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LINKS
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FORMULA
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G.f.: x*(1 + 9*x - 6*x^2 - 6*x^3 + 9*x^4 - x^5 - 4*x^6 + 2*x^7) / ((1 - x)^4*(1 + x)^2).
a(n) = (1/12)*(2*n^3 + 12*n^2 + 28*n - 12) for n>2 and even.
a(n) = (1/12)*(2*n^3 + 12*n^2 + 22*n - 24) for n>2 and odd.
a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n>8.
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PROG
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(PARI) Vec(x*(1 + 9*x - 6*x^2 - 6*x^3 + 9*x^4 - x^5 - 4*x^6 + 2*x^7) / ((1 - x)^4*(1 + x)^2) + O(x^50)) \\ Colin Barker, Nov 14 2017
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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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