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A181890
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a(n) = 8*n^2 + 14*n + 5.
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7
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5, 27, 65, 119, 189, 275, 377, 495, 629, 779, 945, 1127, 1325, 1539, 1769, 2015, 2277, 2555, 2849, 3159, 3485, 3827, 4185, 4559, 4949, 5355, 5777, 6215, 6669, 7139, 7625, 8127, 8645, 9179, 9729, 10295, 10877
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OFFSET
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0,1
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COMMENTS
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First 16 terms of clockwise spiral for odd numbers are as follows:
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13--15--17--19
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11 1---3 21
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9---7---5 23
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31--29--27--25
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a(n) comes from the third vertical.
Sequence found by reading the line from 5, in the direction 5, 27, in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Dec 25 2011
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LINKS
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FORMULA
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a(n) = (2*n+1)*(4*n+5).
a(n) = a(n-1) + 16*n + 6;
a(n) = 2*a(n-1) - a(n-2) + 16.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
Sum_{n>=0} 1/a(n) = 2/3 - Pi/12 - log(2)/6 = 0.289342748774193011891907697817...
Sum_{n>=0} (-1)^n / a(n) = (1 + sqrt(2))*Pi/12 - 2/3 - sqrt(2)*log(tan(Pi/8))/6 = 0.173114712692423461587883724528539... (End)
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MATHEMATICA
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CoefficientList[Series[(5 + 12 x - x^2)/(1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, May 23 2014 *)
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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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STATUS
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approved
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