cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A226372 Number of tilings of an 8 X n rectangle using integer-sided square tiles of area > 1.

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%I A226372 #11 Sep 05 2021 21:59:47
%S A226372 1,0,1,0,5,0,16,0,48,0,160,0,511,0,1651,2,5341,4,17260,22,55846,92,
%T A226372 180658,322,584545,1240,1891519,4520,6120813,16202,19807322,57956,
%U A226372 64098350,204762,207430088,718472,671273411,2506702,2172343071,8697828,7030048159
%N A226372 Number of tilings of an 8 X n rectangle using integer-sided square tiles of area > 1.
%H A226372 Alois P. Heinz, <a href="/A226372/b226372.txt">Table of n, a(n) for n = 0..1000</a>
%F A226372 G.f.: -(x-1) *(x+1) *(x^3+x-1) *(x^3+x+1) *(x^11 -x^10 +x^9 -x^8 +x^7 -2*x^6 -x^5 +x^4 -x^3 +x^2 -x+1) / (x^27 -x^26 +5*x^25 -5*x^24 +9*x^23 -8*x^22 +3*x^21 -5*x^20 -18*x^19 +12*x^18 -29*x^17 +29*x^16 -17*x^15 +32*x^14 +16*x^13 -13*x^12 +25*x^11 -28*x^10 +15*x^9 -18*x^8 -4*x^7 +5*x^6 -5*x^5 +5*x^4 -2*x^3 +2*x^2 +x-1).
%e A226372 a(4) = 5:
%e A226372 ._._._._.  ._._._._.  ._._._._.  ._._._._.  ._._._._.
%e A226372 |       |  |   |   |  |   |   |  |       |  |   |   |
%e A226372 |       |  |___|___|  |___|___|  |       |  |___|___|
%e A226372 |       |  |   |   |  |       |  |       |  |   |   |
%e A226372 |_______|  |___|___|  |       |  |_______|  |___|___|
%e A226372 |       |  |       |  |       |  |   |   |  |   |   |
%e A226372 |       |  |       |  |_______|  |___|___|  |___|___|
%e A226372 |       |  |       |  |   |   |  |   |   |  |   |   |
%e A226372 |_______|  |_______|  |___|___|  |___|___|  |___|___|
%p A226372 a:= n-> coeff(series(-(x-1) *(x+1) *(x^3+x-1) *(x^3+x+1) *(x^11 -x^10 +x^9 -x^8 +x^7 -2*x^6 -x^5 +x^4 -x^3 +x^2 -x+1) / (x^27 -x^26 +5*x^25 -5*x^24 +9*x^23 -8*x^22 +3*x^21 -5*x^20 -18*x^19 +12*x^18 -29*x^17 +29*x^16 -17*x^15 +32*x^14 +16*x^13 -13*x^12 +25*x^11 -28*x^10 +15*x^9 -18*x^8 -4*x^7 +5*x^6 -5*x^5 +5*x^4 -2*x^3 +2*x^2 +x-1), x, n+1), x, n):
%p A226372 seq(a(n), n=0..60);
%Y A226372 Column k=8 of A226206.
%K A226372 nonn,easy
%O A226372 0,5
%A A226372 _Alois P. Heinz_, Jun 05 2013