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A164900
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a(2n) = 4*n*(n+1) + 3; a(2n+1) = 2*n*(n+2) + 3.
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2
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3, 3, 11, 9, 27, 19, 51, 33, 83, 51, 123, 73, 171, 99, 227, 129, 291, 163, 363, 201, 443, 243, 531, 289, 627, 339, 731, 393, 843, 451, 963, 513, 1091, 579, 1227, 649, 1371, 723, 1523, 801, 1683, 883, 1851, 969, 2027, 1059, 2211, 1153
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OFFSET
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0,1
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COMMENTS
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a(n) is also the denominator of the (n+1)-st largest circle in a special case of the Pappus chain inspired by the Yin-Yang symbol. See illustration in the links. - Kival Ngaokrajang, Jun 20 2015
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LINKS
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FORMULA
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G.f.: ( -3-3*x-2*x^2-3*x^4-x^5 ) / ( (x-1)^3*(1+x)^3 ). - R. J. Mathar, Jan 21 2011
a(n) = numerator(((n+1)^2 + 2)/2).
Sum_{n>=0} 1/a(n) = (coth(Pi/sqrt(2))*Pi/sqrt(2) + tanh(Pi/sqrt(2))*Pi/(2*sqrt(2)) - 1)/2. (End)
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MATHEMATICA
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LinearRecurrence[{0, 3, 0, -3, 0, 1}, {3, 3, 11, 9, 27, 19}, 50] (* Amiram Eldar, Aug 09 2022 *)
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PROG
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(PARI) vector(100, n, n--; (1/4)*((-1)^n+3)*(n^2+2*n+3)) \\ Derek Orr, Jun 27 2015
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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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