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

Author

Dimitris Valianatos, Jun 24 2017

Keywords

• nonn

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).

Crossrefs

Cf. A033566, A033567.

Programs

Magma

[2*n^2+n-(n+1) mod 2: n in [1..60]]; // Vincenzo Librandi, Aug 12 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 *)

PARI

{for(n=1,100,print1(2*n^2+n-(n+1)%2", "))}

Formula

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