A321220 a(n) = n+2 if n is even, otherwise a(n) = 2*n+1 if n is odd.

2, 3, 4, 7, 6, 11, 8, 15, 10, 19, 12, 23, 14, 27, 16, 31, 18, 35, 20, 39, 22, 43, 24, 47, 26, 51, 28, 55, 30, 59, 32, 63, 34, 67, 36, 71, 38, 75, 40, 79, 42, 83, 44, 87, 46, 91, 48, 95, 50, 99, 52, 103, 54, 107, 56, 111, 58, 115, 60, 119, 62, 123, 64, 127, 66

Offset

0,1

Comments

For n >= 3, a(n) is the Harborth Constant for the Dihedral groups D2n. See Balachandra link, Theorem 1 p. 2.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Niranjan Balachandran, Eshita Mazumdar, Kevin Zhao, The Harborth Constant for Dihedral Groups, arXiv:1803.08286 [math.CO], 2018.

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

Formula

a(n) = A043547(n+1) + 1.

From Colin Barker, Oct 31 2018: (Start)

G.f.: (2 + 3*x + x^3) / (1-x^2)^2.

a(n) = 2*a(n-2) - a(n-4) for n > 3.

(End)

Maple

a:=n->`if`(modp(n, 2)=0, n+2, 2*n+1): seq(a(n), n=0..70); # Muniru A Asiru, Oct 31 2018

Mathematica

CoefficientList[Series[(2 + 3 x + x^3)/(1 - x^2)^2, {x, 0, 64}], x] (* Michael De Vlieger, Oct 31 2018 *)
Table[If[OddQ[n], (2 n + 1), n + 2], {n, 0, 80}] (* Vincenzo Librandi, Nov 01 2018 *)

Prog

(PARI) a(n) = if (n%2, 2*n+1, n+2);
(PARI) Vec((2 + 3*x + x^3) / ((1 - x)^2*(1 + x)^2) + O(x^80)) \\ Colin Barker, Oct 31 2018
(Magma) [IsOdd(n) select (2*n+1) else n+2: n in [0..80]]; // Vincenzo Librandi, Nov 01 2018

Crossrefs

A299174 and A004767 interleaved.

Cf. A043547, A114752.

Sequence in context: A106442 A091204 A106446 * A036467 A006875 A064554

Adjacent sequences: A321217 A321218 A321219 * A321221 A321222 A321223

Keyword

nonn,easy

Author

Michel Marcus, Oct 31 2018

Status

approved