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A287057 a(n) = 2*n^2 + n - (n+1) mod 2. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 24 11:38 EDT 2020. Contains 337318 sequences. (Running on oeis4.)