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A226369 Number of tilings of a 5 X n rectangle using integer-sided square tiles of area > 1. 2
1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 4, 4, 0, 0, 1, 6, 12, 8, 0, 1, 8, 24, 32, 16, 1, 10, 40, 80, 80, 33, 12, 60, 160, 240, 193, 78, 84, 280, 560, 673, 464, 240, 448, 1120, 1793, 1810, 1168, 928, 2016, 4033, 5396, 4788, 3264, 3872, 8065, 13462, 15580, 12840, 10400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

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

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

FORMULA

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

a(n) = a(n-5)+2*a(n-6) for n>5, a(0) = a(5) = 1, a(1) = a(2) = a(3) = a(4) = 0.

EXAMPLE

a(6) = 2:

._._._._._._.    ._._._._._._.

|     |     |    |   |   |   |

|     |     |    |___|___|___|

|_____|_____|    |     |     |

|   |   |   |    |     |     |

|___|___|___|    |_____|_____|

MAPLE

a:= n-> (Matrix(6, (i, j)-> `if`(i+1=j, 1,

    `if`(i=6, [2, 1, 0$4][j], 0)))^n. <<1, [0$4][], 1>>)[1, 1]:

seq(a(n), n=0..70);

CROSSREFS

Column k=5 of A226206.

Sequence in context: A191906 A187080 A301342 * A320751 A263764 A325668

Adjacent sequences:  A226366 A226367 A226368 * A226370 A226371 A226372

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Jun 05 2013

STATUS

approved

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Last modified August 12 00:34 EDT 2022. Contains 356067 sequences. (Running on oeis4.)