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A244806
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The 180-degree spoke (or ray) of a hexagonal spiral of Ulam.
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7
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1, 18, 59, 124, 213, 326, 463, 624, 809, 1018, 1251, 1508, 1789, 2094, 2423, 2776, 3153, 3554, 3979, 4428, 4901, 5398, 5919, 6464, 7033, 7626, 8243, 8884, 9549, 10238, 10951, 11688, 12449, 13234, 14043, 14876, 15733, 16614, 17519, 18448, 19401, 20378, 21379, 22404, 23453, 24526, 25623
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listen;
history;
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 12*n^2 - 19*n + 8.
See A056105 example section for its formula.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
G.f.: x*(1 + 15*x + 8*x^2) / (1 - x)^3.
(End)
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EXAMPLE
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See A056105 example section for its diagram.
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MAPLE
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MATHEMATICA
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f[n_] := 12n^2 - 19n + 8; Array[f, 47]
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PROG
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(PARI) vector(50, n, 12*n^2 - 19*n + 8) \\ Michel Marcus, Jul 06 2014
(PARI) Vec(x*(1 + 15*x + 8*x^2) / (1 - x)^3 + O(x^50)) \\ Colin Barker, Dec 12 2016
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CROSSREFS
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Cf. A056105, A244802, A056106, A244803, A056107, A244804, A056108, A244805, A056109, A003215, A033577.
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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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