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A220123 Number of tilings of a 4 X n rectangle using integer sided rectangular tiles of area 4. 2
1, 1, 2, 3, 9, 16, 35, 65, 143, 281, 590, 1174, 2440, 4925, 10142, 20563, 42178, 85819, 175632, 357875, 731536, 1491966, 3047879, 6218844, 12699982, 25919176, 52922491, 108022099, 220541999, 450186874, 919074255, 1876149465, 3830134125, 7818778884, 15961716918 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Caleb Wagner, Number of tilings of a 4 X n rectangle using integer sided rectangular tiles of area 4

FORMULA

G.f.: -(x-1)*(x+1)*(x^2+1) / (x^8-x^6+x^5-5*x^4-x^2-x+1).

a(n) = a(n-1)+a(n-2)+5*a(n-4)-a(n-5)+a(n-6)-a(n-8). - Caleb Wagner, Nov 06 2013

EXAMPLE

a(3) = 3, because there are 3 tilings of a 4 X 3 rectangle using integer sided rectangular tiles of area 4:

._._._.   ._.___.   .___._.

| | | |   | |   |   |   | |

| | | |   | |___|   |___| |

| | | |   | |   |   |   | |

|_|_|_|   |_|___|   |___|_|

MAPLE

gf:= -(x-1)*(x+1)*(x^2+1)/(x^8-x^6+x^5-5*x^4-x^2-x+1):

a:= n-> coeff(series(gf, x, n+1), x, n):

seq(a(n), n=0..50);

CROSSREFS

Column k=4 of A220122.

Sequence in context: A173809 A298355 A023147 * A220125 A095742 A011951

Adjacent sequences:  A220120 A220121 A220122 * A220124 A220125 A220126

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Dec 05 2012

STATUS

approved

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Last modified April 10 20:14 EDT 2021. Contains 342856 sequences. (Running on oeis4.)