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A001545
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a(n) = (5n+1)*(5n+4).
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2
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4, 54, 154, 304, 504, 754, 1054, 1404, 1804, 2254, 2754, 3304, 3904, 4554, 5254, 6004, 6804, 7654, 8554, 9504, 10504, 11554, 12654, 13804, 15004, 16254, 17554, 18904, 20304, 21754, 23254, 24804, 26404, 28054, 29754, 31504, 33304, 35154, 37054, 39004, 41004
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OFFSET
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0,1
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LINKS
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FORMULA
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Sum_{n>=0} 1/a(n) = sqrt(1 + 2/sqrt(5))*Pi/15 = 0.2882687....
Sum_{n>=0} (-1)^n/a(n) = 2*log(phi)/(3*sqrt(5)) + 2*log(2)/15, where phi is the golden ratio (A001622).
Product_{n>=0} (1 - 1/a(n)) = sqrt(2 + 2/sqrt(5)) * cos(sqrt(13)*Pi/10).
Product_{n>=0} (1 + 1/a(n)) = sqrt(2 + 2/sqrt(5)) * cos(Pi/(2*sqrt(5))).
Product_{n>=0} (1 + 2/a(n)) = phi. (End)
G.f.: -2*(2+21*x+2*x^2)/(x-1)^3 . - R. J. Mathar, May 30 2022
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MATHEMATICA
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Table[(5n+1)(5n+4), {n, 0, 60}] (* or *) LinearRecurrence[{3, -3, 1}, {4, 54, 154}, 60] (* Harvey P. Dale, Mar 17 2019 *)
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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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