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A336732
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The number of tight 4 X n pavings.
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4
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0, 1, 26, 282, 2072, 12279, 63858, 305464, 1382648, 6029325, 25628762, 107026662, 441439944, 1804904755, 7334032754, 29669499492, 119647095176, 481400350185, 1933747745850, 7758556171570, 31102292517560, 124605486285231, 498987240470066, 1997573938402512
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OFFSET
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0,3
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COMMENTS
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This is row (or column) m=4 of the array T in A285357.
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LINKS
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D. E. Knuth (Proposer), Problem 12005, Amer. Math. Monthly 124 (No. 8, Oct. 2017), page 755. For the solution see op. cit., 126 (No. 7, 2019), 660-664.
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FORMULA
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a(n) = (4^(n+5)+(n-42)*3^(n+4)-9*(2*n-27)*2^(n+5)-36*n^3-486*n^2-2577*n-5398)/36.
G.f.: (x+8*x^2-47*x^3+6*x^4+104*x^5)/((1-x)^4*(1-2*x)^2*(1-3*x)^2*(1-4*x)).
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MAPLE
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seq((4^(n+5)+(n-42)*3^(n+4)-9*(2*n-27)*2^(n+5)-36*n^3-486*n^2-2577*n-5398)/36, n=0..20);
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MATHEMATICA
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num=(x+8*x^2-47*x^3+6*x^4+104*x^5); den=((1-x)^4*(1-2*x)^2*(1-3*x)^2*(1-4*x)); CoefficientList[Series[num/den, {x, 0, 20}], x]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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