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A287057
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a(n) = 2*n^2 + n - (n+1) mod 2.
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1
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3, 9, 21, 35, 55, 77, 105, 135, 171, 209, 253, 299, 351, 405, 465, 527, 595, 665, 741, 819, 903, 989, 1081, 1175, 1275, 1377, 1485, 1595, 1711, 1829, 1953, 2079, 2211, 2345, 2485, 2627, 2775, 2925, 3081, 3239, 3403, 3569, 3741, 3915, 4095
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OFFSET
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1,1
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COMMENTS
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Let r(n) = (a(n)-1)/a(n) if n mod 2 = 1, (a(n)+1)/a(n) otherwise; then Product_{n>=1} r(n) = (2/3) * (10/9) * (20/21) * (36/35) * (54/55) * (78/77) * (104/105) * (136/135) * ... = agm(1,sqrt(2))^2/2 = 0.7177700110461299978211932237.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
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FORMULA
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G.f.: x*(3+3*x+3*x^2-x^3)/((1+x)*(1-x)^3). - Robert Israel, Aug 11 2017
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MAPLE
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seq(2*n^2 + n - ((n+1) mod 2), n = 1 .. 30); # Robert Israel, Aug 11 2017
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MATHEMATICA
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a[n_] := 2 n^2 + n - Mod[n + 1, 2]; Array[a, 50] (* Robert G. Wilson v, Aug 10 2017 *)
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PROG
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(PARI) {for(n=1, 100, print1(2*n^2+n-(n+1)%2", "))}
(MAGMA) [2*n^2+n-(n+1) mod 2: n in [1..60]]; // Vincenzo Librandi, Aug 12 2017
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CROSSREFS
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Cf. A033566, A033567.
Sequence in context: A031886 A147458 A169927 * A048780 A009864 A128127
Adjacent sequences: A287054 A287055 A287056 * A287058 A287059 A287060
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KEYWORD
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nonn
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AUTHOR
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Dimitris Valianatos, Jun 24 2017
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STATUS
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approved
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