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A278330 Number of tilings of a 5 X n rectangle using n pentominoes of shapes P, U, X. 5
1, 0, 2, 1, 12, 10, 59, 52, 276, 349, 1404, 1984, 7019, 11148, 35686, 62181, 182776, 339350, 942507, 1841208, 4887096, 9921685, 25442304, 53190380, 132928715, 284198328, 696276202, 1514363221, 3654567764, 8053235650, 19212546163, 42762014028, 101125071372 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Wikipedia, Pentomino

Index entries for linear recurrences with constant coefficients, signature (0,2,2,8,4,21,-8,-4,-6,0,-16,-8).

FORMULA

G.f.: -(4*x^6+x^3-1) / (8*x^12 +16*x^11 +6*x^9 +4*x^8 +8*x^7 -21*x^6 -4*x^5 -8*x^4 -2*x^3 -2*x^2+1).

a(n) mod 2 = A079978(n).

EXAMPLE

a(2) = 2,          a(3) = 1:

.___.   .___.      ._____.

|   |   |   |      | ._. |

| ._|   |_. |      |_| |_|

|_| |   | |_|      |_   _|

|   |   |   |      | |_| |

|___|   |___|      |_____| .

MAPLE

a:= n-> (Matrix(12, (i, j)-> `if`(i+1=j, 1, `if`(i=12,

    [-8, -16, 0, -6, -4, -8, 21, 4, 8, 2, 2, 0][j], 0)))^n.

    <<1, 0, 2, 1, 12, 10, 59, 52, 276, 349, 1404, 1984>>)[1, 1]:

seq(a(n), n=0..35);

CROSSREFS

Cf. A079978, A174249, A233427, A234312, A234931, A247124, A247268, A247443, A249762, A264765, A264812.

Sequence in context: A217109 A297967 A199930 * A048854 A151508 A164826

Adjacent sequences:  A278327 A278328 A278329 * A278331 A278332 A278333

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Nov 18 2016

STATUS

approved

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Last modified February 19 09:33 EST 2020. Contains 332041 sequences. (Running on oeis4.)