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A243645
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Number of ways two L-tiles can be placed on an n X n square.
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3
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0, 0, 0, 1, 20, 87, 244, 545, 1056, 1855, 3032, 4689, 6940, 9911, 13740, 18577, 24584, 31935, 40816, 51425, 63972, 78679, 95780, 115521, 138160, 163967, 193224, 226225, 263276, 304695, 350812, 401969, 458520, 520831, 589280, 664257, 746164, 835415, 932436
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OFFSET
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0,5
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COMMENTS
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This sequence also represents the number of edges added to G so that it is complete, where G is a graph of (n-1)^2 nodes arranged in a rhombus and embedded in the hexagonal lattice. G begins with A045944(n-2) edges and a(n) edges are added to form a complete graph. - John Tyler Rascoe, Sep 24 2022
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LINKS
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FORMULA
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G.f.: x^3*(x^3+3*x^2-15*x-1) / (x-1)^5.
a(n) = (n^4-4*n^3-n^2+18*n-16)/2 for n>=2, a(n) = 0 for n<2.
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EXAMPLE
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a(3) = 1:
._____.
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|___|_| .
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MAPLE
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a:= n-> `if`(n<2, 0, ((((n-4)*n-1)*n+18)*n-16)/2):
seq(a(n), n=0..50);
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MATHEMATICA
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CoefficientList[Series[x^3 (x^3+3x^2-15x-1)/(x-1)^5, {x, 0, 40}], x] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 0, 1, 20, 87, 244}, 40] (* Harvey P. Dale, Mar 06 2016 *)
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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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