A309118 Number of tiles added at iteration n when successively, layer by layer, building a symmetric patch of a rhombille tiling around a central star of six rhombs.

6, 6, 12, 18, 24, 24, 36, 30, 48, 36, 60, 42, 72, 48, 84, 54, 96, 60, 108, 66, 120, 72, 132, 78, 144, 84, 156, 90, 168, 96, 180, 102, 192, 108, 204, 114, 216, 120, 228, 126, 240, 132, 252, 138, 264, 144, 276, 150, 288, 156, 300, 162, 312, 168, 324, 174, 336

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Felix Fröhlich, Layers in the rhombille tiling, 2019.

Wikipedia, Rhombille tiling

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

Formula

a(2*n+1) = A008594(n).

a(2*n) = A008588(n+1) for n > 1.

From Colin Barker, Jul 13 2019: (Start)

G.f.: 6*x*(1 + x + x^3 + x^4 - x^5) / ((1 - x)^2*(1 + x)^2).

a(n) = 2*a(n-2) - a(n-4) for n>6.

(End)

Example

See illustration in Fröhlich, 2019.

Mathematica

Join[{6, 6}, LinearRecurrence[{0, 2, 0, -1}, {12, 18, 24, 24}, 60]] (* Vincenzo Librandi, Jul 16 2019 *)

Prog

(PARI) a(n) = if(n<3, 6, if(n%2==0, 6*((n+2)/2), 12*((n-1)/2)))
(PARI) Vec(6*x*(1 + x + x^3 + x^4 - x^5) / ((1 - x)^2*(1 + x)^2) + O(x^40)) \\ Colin Barker, Jul 13 2019
(Magma) I:=[6, 6, 12, 18, 24, 24]; [n le 6 select I[n] else 2*Self(n-2)-Self(n-4): n in [1..60]]; // Vincenzo Librandi, Jul 16 2019

Crossrefs

Cf. A008588, A008594.

Cf. A242128 (5-fold, Star), A242129 (5-fold, Sun), A242888 (7-fold, Star), A242889 (7-fold, Sun), A242890 (8-fold, Star), A242891 (8-fold, Sun), A242892 (9-fold, Star), A242893 (9-fold, Sun), A242894 (Kite and dart, Star), A242895 (Kite and dart, Sun).

Sequence in context: A315789 A315790 A315791 * A315792 A315793 A315794

Adjacent sequences: A309115 A309116 A309117 * A309119 A309120 A309121

Keyword

nonn,easy

Author

Felix Fröhlich, Jul 13 2019

Status

approved