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A247076 Number of tilings of a 5 X 2n rectangle using 2n pentominoes of shape P. 3
1, 2, 6, 20, 62, 194, 612, 1922, 6038, 18980, 59646, 187442, 589076, 1851266, 5817894, 18283700, 57459518, 180575906, 567489348, 1783428098, 5604714422, 17613731780, 55354032894, 173959101458, 546694927604, 1718078222594, 5399341807686, 16968314698580 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Pentomino

Index entries for linear recurrences with constant coefficients, signature (2,2,5).

FORMULA

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

a(n) = 2*a(n-1)+2*a(n-2)+5*a(n-3) for n>3, a(0)=1; a(1)=2, a(2)=6, a(3)=20.

EXAMPLE

a(2) = 6:

._______. ._______. ._______. ._______. ._______. ._______.

|   |   | |   |   | |   |   | |   |   | |   ._| | | |_.   |

| ._| ._| |_. |_. | | ._|_. | |_. | ._| |___|   | |   |___|

|_| |_| | | |_| |_| |_| | |_| | |_|_| | |   |___| |___|   |

|   |   | |   |   | |   |   | |   |   | | ._|   | |   |_. |

|___|___| |___|___| |___|___| |___|___| |_|_____| |_____|_| .

MAPLE

a:= proc(n) option remember; `if`(n<4, [1, 2, 6, 20][n+1],

       2*a(n-1) +2*a(n-2) +5*a(n-3))

    end:

seq(a(n), n=0..40);

MATHEMATICA

Join[{1}, LinearRecurrence[{2, 2, 5}, {2, 6, 20}, 40]] (* Jean-Fran├žois Alcover, May 29 2018 *)

CROSSREFS

Even bisection of main diagonal of A247706.

Cf. A174249, A233427, A247121.

Sequence in context: A263900 A260696 A052958 * A177792 A193235 A199102

Adjacent sequences:  A247073 A247074 A247075 * A247077 A247078 A247079

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 17 2014

STATUS

approved

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Last modified November 22 18:55 EST 2019. Contains 329410 sequences. (Running on oeis4.)