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A220132 Number of tilings of an n X 7 rectangle using integer-sided rectangular tiles of area n.

%I A220132 #18 Sep 05 2021 19:18:53
%S A220132 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,
%T A220132 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,
%U A220132 65,1,88,4,66,9,21,1,185,1,21,10,65,4,88,1,65,9,27,1
%N A220132 Number of tilings of an n X 7 rectangle using integer-sided rectangular tiles of area n.
%C A220132 1 followed by period 420: (1, 21, ..., 186) repeated; offset 0.
%H A220132 Alois P. Heinz, <a href="/A220132/b220132.txt">Table of n, a(n) for n = 0..1000</a>
%F A220132 G.f.: see Maple program.
%e A220132 a(5) = 4, because there are 4 tilings of a 5 X 7 rectangle using integer-sided rectangular tiles of area 5:
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%p A220132 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) /
%p A220132 (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):
%p A220132 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A220132 seq(a(n), n=0..100);
%Y A220132 Row n=7 of A220122.
%K A220132 nonn,easy
%O A220132 0,3
%A A220132 _Alois P. Heinz_, Dec 06 2012