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A220132 Number of tilings of an n X 7 rectangle using integer sided rectangular tiles of area n. 2
1, 1, 21, 9, 65, 4, 88, 2, 65, 9, 26, 1, 180, 1, 22, 12, 65, 1, 88, 1, 70, 10, 21, 1, 180, 4, 21, 9, 66, 1, 93, 1, 65, 9, 21, 5, 180, 1, 21, 9, 70, 1, 89, 1, 65, 12, 21, 1, 180, 2, 26, 9, 65, 1, 88, 4, 66, 9, 21, 1, 185, 1, 21, 10, 65, 4, 88, 1, 65, 9, 27, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

1 followed by period 420: (1, 21, ..., 186) repeated; offset 0.

LINKS

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

FORMULA

G.f.: see Maple program.

EXAMPLE

a(5) = 4, because there are 4 tilings of a 5 X 7 rectangle using integer sided rectangular tiles of area 5:

._._._._._._._.  ._________._._.

| | | | | | | |  |_________| | |

| | | | | | | |  |_________| | |

| | | | | | | |  |_________| | |

| | | | | | | |  |_________| | |

|_|_|_|_|_|_|_|  |_________|_|_|

._._________._.  ._._._________.

| |_________| |  | | |_________|

| |_________| |  | | |_________|

| |_________| |  | | |_________|

| |_________| |  | | |_________|

|_|_________|_|  |_|_|_________|

MAPLE

gf:= -(185*x^26 +186*x^25 +392*x^24 +402*x^23 +673*x^22 +687*x^21 +1046*x^20 +877*x^19 +1300*x^18 +1119*x^17 +1374*x^16 +1128*x^15 +1353*x^14 +1010*x^13 +1169*x^12 +760*x^11 +822*x^10 +567*x^9 +564*x^8 +325*x^7 +310*x^6 +135*x^5 +121*x^4 +34*x^3 +24*x^2 +2*x +1) /

(x^26 +x^25 +2*x^24 +2*x^23 +3*x^22 +3*x^21 +4*x^20 +3*x^19 +4*x^18 +3*x^17 +3*x^16 +2*x^15 +x^14 -x^12 -2*x^11 -3*x^10 -3*x^9 -4*x^8 -3*x^7 -4*x^6 -3*x^5 -3*x^4 -2*x^3 -2*x^2 -x -1):

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

seq(a(n), n=0..100);

CROSSREFS

Row n=7 of A220122.

Sequence in context: A040426 A040425 A040424 * A146375 A040423 A318648

Adjacent sequences:  A220129 A220130 A220131 * A220133 A220134 A220135

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Dec 06 2012

STATUS

approved

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Last modified October 13 16:10 EDT 2019. Contains 327966 sequences. (Running on oeis4.)