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A220133 Number of tilings of an n X 8 rectangle using integer-sided rectangular tiles of area n. 2

%I

%S 1,1,34,13,143,5,209,3,250,13,44,1,472,1,36,19,250,1,209,1,153,15,34,

%T 1,681,5,34,13,145,1,221,1,250,13,34,7,472,1,34,13,260,1,211,1,143,19,

%U 34,1,681,3,44,13,143,1,209,5,252,13,34,1,484,1,34,15,250,5

%N Number of tilings of an n X 8 rectangle using integer-sided rectangular tiles of area n.

%C 1 followed by period 840: (1, 34, ..., 695) repeated; offset 0.

%H Alois P. Heinz, <a href="/A220133/b220133.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: see Maple program.

%e a(5) = 5, because there are 5 tilings of a 5 X 8 rectangle using integer-sided rectangular tiles of area 5:

%e ._._._._._._._._. ._________._._._. ._._________._._.

%e | | | | | | | | | |_________| | | | | |_________| | |

%e | | | | | | | | | |_________| | | | | |_________| | |

%e | | | | | | | | | |_________| | | | | |_________| | |

%e | | | | | | | | | |_________| | | | | |_________| | |

%e |_|_|_|_|_|_|_|_| |_________|_|_|_| |_|_________|_|_|

%e ._._._________._. ._._._._________.

%e | | |_________| | | | | |_________|

%e | | |_________| | | | | |_________|

%e | | |_________| | | | | |_________|

%e | | |_________| | | | | |_________|

%e |_|_|_________|_| |_|_|_|_________|

%p gf:= -(694*x^46 +x^45 +728*x^44 +708*x^43 +872*x^42 +1441*x^41 +1789*x^40 +928*x^39 +2784*x^38 +1967*x^37 +2307*x^36 +3029*x^35 +3122*x^34 +2593*x^33 +4196*x^32 +2514*x^31 +3854*x^30 +3978*x^29 +3762*x^28

%p +3055*x^27 +4448*x^26 +2969*x^25 +4154*x^24 +3352*x^23 +3461*x^22 +2969*x^21 +3755*x^20 +2362*x^19 +3069*x^18 +2592*x^17 +2468*x^16 +1821*x^15 +2117*x^14 +1207*x^13 +1736*x^12 +950*x^11 +921*x^10 +581*x^9 +705*x^8 +235*x^7 +403*x^6 +55*x^5 +179*x^4 +15*x^3 +35*x^2 +x +1) /

%p (x^46 +x^44 +x^43 +x^42 +2*x^41 +2*x^40 +x^39 +3*x^38 +2*x^37 +2*x^36 +3*x^35 +2*x^34 +2*x^33 +3*x^32 +x^31 +2*x^30 +2*x^29 +x^28 +x^27 +x^26

%p +x^24 -x^22 -x^20 -x^19 -x^18 -2*x^17 -2*x^16 -x^15 -3*x^14 -2*x^13 -2*x^12 -3*x^11 -2*x^10 -2*x^9 -3*x^8 -x^7 -2*x^6 -2*x^5 -x^4 -x^3 -x^2 -1):

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

%p seq(a(n), n=0..80);

%Y Row n=8 of A220122.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Dec 06 2012

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Last modified December 6 10:24 EST 2021. Contains 349563 sequences. (Running on oeis4.)