The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A278330

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A278330

Number of tilings of a 5 X n rectangle using n pentominoes of shapes P, U, X.
(history; published version)

#12 by Alois P. Heinz at Mon Feb 06 12:28:12 EST 2017

STATUS

editing

approved

#11 by Alois P. Heinz at Mon Feb 06 12:28:07 EST 2017

LINKS

Wikipedia, <a href="httphttps://en.wikipedia.org/wiki/Pentomino">Pentomino</a>

STATUS

approved

editing

#10 by Alois P. Heinz at Thu Nov 24 07:14:25 EST 2016

STATUS

editing

approved

#9 by Alois P. Heinz at Wed Nov 23 11:19:18 EST 2016

FORMULA

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

CROSSREFS

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

#8 by Alois P. Heinz at Wed Nov 23 11:09:13 EST 2016

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).

#7 by Alois P. Heinz at Wed Nov 23 11:06:59 EST 2016

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);

#6 by Alois P. Heinz at Fri Nov 18 12:27:37 EST 2016

LINKS

<a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,8,4,21,-8,-4,-6,0,-16,-8).

#5 by Alois P. Heinz at Fri Nov 18 12:24:14 EST 2016

LINKS

Alois P. Heinz, <a href="/A278330/b278330.txt">Table of n, a(n) for n = 0..1000</a>

KEYWORD

nonn,easy,changed

#4 by Alois P. Heinz at Fri Nov 18 12:11:27 EST 2016

CROSSREFS

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

#3 by Alois P. Heinz at Fri Nov 18 12:08:57 EST 2016

EXAMPLE

a(2) = 2, a(3) = 1:

.___. .___. ._____.

| | | | | ._. |

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

|_| | | |_| |_ _|

| | | | | |_| |

|___| |___| |_____| .