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A145910
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a(n) = (1 + 3*n)*(4 + 3*n)/2.
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3
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2, 14, 35, 65, 104, 152, 209, 275, 350, 434, 527, 629, 740, 860, 989, 1127, 1274, 1430, 1595, 1769, 1952, 2144, 2345, 2555, 2774, 3002, 3239, 3485, 3740, 4004, 4277, 4559, 4850, 5150, 5459, 5777, 6104, 6440, 6785, 7139, 7502, 7874
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OFFSET
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0,1
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REFERENCES
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R. C. Alperin, A nonlinear recurrence and its relations to Chebyshev polynomials, Fib. Q., Vol. 58, No. 2 (2020), pp. 140-142.
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LINKS
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FORMULA
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a(n) = a(n-1) + 3*(3n+1) = a(n-1) + A017197(n+1).
a(n) = 2*a(n-1) - a(n-2) + 9.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
Sum_{n>=0} 1/a(n) = 2/3.
Sum_{n>=0} (-1)^n/a(n) = 4*Pi/(9*sqrt(3)) + 4*log(2)/9 - 2/3. (End)
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MAPLE
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MATHEMATICA
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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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