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A220134 Number of tilings of an n X 9 rectangle using integer-sided rectangular tiles of area n. 2
1, 1, 55, 19, 281, 6, 473, 4, 495, 37, 75, 1, 1091, 1, 60, 30, 495, 1, 609, 1, 309, 22, 55, 1, 1509, 6, 55, 37, 286, 1, 499, 1, 495, 19, 55, 9, 1259, 1, 55, 19, 523, 1, 478, 1, 281, 48, 55, 1, 1509, 4, 75, 19, 281, 1, 609, 6, 500, 19, 55, 1, 1125, 1, 55, 40 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

1 followed by period 2520: (1, 55, ..., 1716) repeated; offset 0.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2520

FORMULA

G.f.: see Maple program.

EXAMPLE

a(7) = 4, because there are 4 tilings of a 7 X 9 rectangle using integer-sided rectangular tiles of area 7:

._._._._._._._._._.   ._____________._._.

| | | | | | | | | |   |_____________| | |

| | | | | | | | | |   |_____________| | |

| | | | | | | | | |   |_____________| | |

| | | | | | | | | |   |_____________| | |

| | | | | | | | | |   |_____________| | |

| | | | | | | | | |   |_____________| | |

|_|_|_|_|_|_|_|_|_|   |_____________|_|_|

._._____________._.   ._._._____________.

| |_____________| |   | | |_____________|

| |_____________| |   | | |_____________|

| |_____________| |   | | |_____________|

| |_____________| |   | | |_____________|

| |_____________| |   | | |_____________|

| |_____________| |   | | |_____________|

|_|_____________|_|   |_|_|_____________|

MAPLE

gf:= -(1715*x^84 -1714*x^83 +1769*x^82 -35*x^81 +2032*x^80 -255*x^79 +2518*x^78 -443*x^77 +4730*x^76 -427*x^75 +4827*x^74 +13*x^73 +9665*x^72 -2709*x^71 +8592*x^70 +1768*x^69 +11758*x^68 -521*x^67 +13222*x^66 -578*x^65 +17124*x^64 +1707*x^63 +15652*x^62 +761*x^61 +24022*x^60

-1869*x^59 +20608*x^58 +3671*x^57 +25352*x^56 +340*x^55 +25138*x^54 +265*x^53 +28854*x^52 +3728*x^51 +25940*x^50 -281*x^49 +33322*x^48 +443*x^47 +26340*x^46 +4094*x^45 +30372*x^44 +578*x^43 +28000*x^42 +578*x^41 +28658*x^40 +4094*x^39 +24626*x^38 -1271*x^37 +28180*x^36

+1433*x^35 +20798*x^34 +2014*x^33 +21998*x^32 +265*x^31 +18282*x^30 +340*x^29 +16782*x^28 +1957*x^27 +13752*x^26 -1869*x^25 +13738*x^24 +761*x^23 +8796*x^22 -7*x^21 +8554*x^20 -578*x^19 +6366*x^18 -521*x^17 +4902*x^16 +54*x^15 +3450*x^14 -995*x^13 +2809*x^12 +13*x^11 +1399*x^10 -427*x^9 +1302*x^8 -443*x^7 +804*x^6 -255*x^5 +318*x^4-35*x^3 +55*x^2+1)/

(x^84 -x^83 +x^82 +x^80 +x^78 +2*x^76 +2*x^74 +4*x^72 -x^71 +3*x^70 +x^69 +4*x^68 +4*x^66 +5*x^64 +x^63 +4*x^62 +6*x^60 +4*x^58 +x^57 +5*x^56 +4*x^54 +4*x^52 +x^51 +3*x^50 -x^49 +3*x^48 +x^47 +x^46 +x^44 -x^40 -x^38

-x^37 -3*x^36 +x^35 -3*x^34 -x^33 -4*x^32 -4*x^30 -5*x^28 -x^27 -4*x^26 -6*x^24 -4*x^22 -x^21 -5*x^20 -4*x^18 -4*x^16 -x^15 -3*x^14 +x^13 -4*x^12 -2*x^10 -2*x^8 -x^6 -x^4 -x^2 +x -1):

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

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

CROSSREFS

Row n=9 of A220122.

Sequence in context: A057965 A083516 A203907 * A178509 A033375 A236416

Adjacent sequences:  A220131 A220132 A220133 * A220135 A220136 A220137

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Dec 06 2012

STATUS

approved

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Last modified November 29 09:10 EST 2021. Contains 349416 sequences. (Running on oeis4.)