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A177072
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a(n) = (9*n+2)*(9*n+7).
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2
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14, 176, 500, 986, 1634, 2444, 3416, 4550, 5846, 7304, 8924, 10706, 12650, 14756, 17024, 19454, 22046, 24800, 27716, 30794, 34034, 37436, 41000, 44726, 48614, 52664, 56876, 61250, 65786, 70484, 75344, 80366, 85550, 90896, 96404, 102074, 107906, 113900, 120056
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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) = 162*n + a(n-1) with n > 0, a(0)=14.
G.f.: 2*(7+67*x+7*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
Sum_{n>=0} 1/a(n) = cot(2*Pi/9)*Pi/45.
Product_{n>=0} (1 - 1/a(n)) = cosec(2*Pi/9)*cos(sqrt(29)*Pi/18).
Product_{n>=0} (1 + 1/a(n)) = cosec(2*Pi/9)*cos(sqrt(21)*Pi/18). (End)
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MATHEMATICA
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CoefficientList[Series[2(7 + 67 x + 7 x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Apr 08 2013 *)
Table[(9*n + 2)*(9*n + 7), {n, 0, 40}] (* Amiram Eldar, Feb 19 2023 *)
LinearRecurrence[{3, -3, 1}, {14, 176, 500}, 50] (* Harvey P. Dale, Jun 10 2023 *)
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PROG
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(Magma) I:=[14, 176, 500]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Apr 08 2013
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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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