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A177065
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a(n) = (8*n+3)*(8*n+5).
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2
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15, 143, 399, 783, 1295, 1935, 2703, 3599, 4623, 5775, 7055, 8463, 9999, 11663, 13455, 15375, 17423, 19599, 21903, 24335, 26895, 29583, 32399, 35343, 38415, 41615, 44943, 48399, 51983, 55695, 59535, 63503, 67599, 71823, 76175, 80655, 85263, 89999, 94863, 99855
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = 128*n+a(n-1) with n>0, a(0)=15.
a(0)=15, a(1)=143, a(2)=399, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Mar 13 2013
Sum_{n>=0} 1/a(n) = (sqrt(2)-1)*Pi/16.
Sum_{n>=0} (-1)^n/a(n) = (cos(Pi/8) * log(tan(3*Pi/16)) + sin(Pi/8) * log(cot(Pi/16)))/4.
Product_{n>=0} (1 - 1/a(n)) = sec(Pi/8)*cos(Pi/(4*sqrt(2))).
Product_{n>=0} (1 + 1/a(n)) = sec(Pi/8). (End)
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MAPLE
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MATHEMATICA
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Table[(8n+3)(8n+5), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {15, 143, 399}, 40] (* Harvey P. Dale, Mar 13 2013 *)
CoefficientList[Series[(15 + 98 x + 15 x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Apr 08 2013 *)
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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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