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A014634
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a(n) = (2*n+1)*(4*n+1).
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24
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1, 15, 45, 91, 153, 231, 325, 435, 561, 703, 861, 1035, 1225, 1431, 1653, 1891, 2145, 2415, 2701, 3003, 3321, 3655, 4005, 4371, 4753, 5151, 5565, 5995, 6441, 6903, 7381, 7875, 8385, 8911, 9453, 10011, 10585, 11175, 11781, 12403, 13041, 13695, 14365, 15051
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OFFSET
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0,2
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COMMENTS
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Sequence found by reading the line from 1, in the direction 1, 15, ..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 03 2011
a(n) is also the sum of natural numbers which can be placed in a center box and expanded ones on 4 arms on N, S, E, W or NE, NW, SW, SE directions. See illustration in links. - Kival Ngaokrajang, Jul 08 2014
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LINKS
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FORMULA
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Sum_{n>=0} 1/a(n) = Pi/4 + log(2)/2.
Sum_{n>=0} (-1)^n/a(n) = Pi*(sqrt(2)-1)/4 + log(sqrt(2)+1)/sqrt(2). (End)
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MAPLE
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1, 15, 45}, 50] (* Harvey P. Dale, Aug 30 2021 *)
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PROG
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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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EXTENSIONS
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STATUS
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approved
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