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A177071
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a(n) = (7*n + 3)*(7*n + 4).
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2
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12, 110, 306, 600, 992, 1482, 2070, 2756, 3540, 4422, 5402, 6480, 7656, 8930, 10302, 11772, 13340, 15006, 16770, 18632, 20592, 22650, 24806, 27060, 29412, 31862, 34410, 37056, 39800, 42642, 45582, 48620, 51756, 54990, 58322, 61752, 65280, 68906, 72630, 76452
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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) = 98*n+a(n-1) with n>0, a(0)=12.
a(0)=12, a(1)=110, a(2)=306, a(n)=3*a(n-1)-3*a(n-2)+a(n-3).
G.f.: -((2*(x+6)*(6*x+1))/(x-1)^3). (End)
Sum_{n>=0} 1/a(n) = tan(Pi/14)*Pi/7.
Product_{n>=0} (1 - 1/a(n)) = sec(Pi/14)*cos(sqrt(5)*Pi/14).
Product_{n>=0} (1 + 1/a(n)) = sec(Pi/14)*cosh(sqrt(3)*Pi/14). (End)
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MATHEMATICA
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Table[(7n+3)(7n+4), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {12, 110, 306}, 40] (* Harvey P. Dale, Oct 09 2011 *)
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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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