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A125201
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a(n) = 8*n^2 - 7*n + 1.
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2
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2, 19, 52, 101, 166, 247, 344, 457, 586, 731, 892, 1069, 1262, 1471, 1696, 1937, 2194, 2467, 2756, 3061, 3382, 3719, 4072, 4441, 4826, 5227, 5644, 6077, 6526, 6991, 7472, 7969, 8482, 9011, 9556, 10117, 10694, 11287, 11896, 12521, 13162, 13819, 14492, 15181
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OFFSET
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1,1
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COMMENTS
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Central terms of the triangle in A125199.
Sequence found by reading the line from 2, in the direction 2, 19, ..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 05 2011
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LINKS
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FORMULA
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a(n) = 1 + A051870(n). - Omar E. Pol, Sep 05 2011
a(1) = 2, a(n) = a(n-1) + 16*n - 15.
a(n) = 2*a(n-1) - a(n-2) + 16 with a(1) = 2 and a(2) = 19.
G.f.: (1 - x + 16*x^2)/(1 - x)^3. (End)
Sum_{n>=1} 1/a(n) = ( psi(9/16+sqrt(17)/16) -psi(9/16-sqrt(17)/16)) /sqrt(17) = 0.61242052... - R. J. Mathar, Apr 22 2024
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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STATUS
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approved
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