A287057 a(n) = 2*n^2 + n - (n+1) mod 2.

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

Offset

1,1

Comments

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.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

G.f.: x*(3+3*x+3*x^2-x^3)/((1+x)*(1-x)^3). - Robert Israel, Aug 11 2017

Maple

seq(2*n^2 + n - ((n+1) mod 2), n = 1 .. 30); # Robert Israel, Aug 11 2017

Mathematica

a[n_] := 2 n^2 + n - Mod[n + 1, 2]; Array[a, 50] (* Robert G. Wilson v, Aug 10 2017 *)

Prog

(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

Crossrefs

Cf. A033566, A033567.

Sequence in context: A031886 A147458 A169927 * A048780 A009864 A128127

Adjacent sequences: A287054 A287055 A287056 * A287058 A287059 A287060

Keyword

nonn

Author

Dimitris Valianatos, Jun 24 2017

Status

approved