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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 1 09:53 EDT 2020. Contains 334762 sequences. (Running on oeis4.)