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A362153
Number of skew shapes in a 3 X n rectangle with no empty rows or columns.
0
1, 8, 29, 73, 151, 276, 463, 729, 1093, 1576, 2201, 2993, 3979, 5188, 6651, 8401, 10473, 12904, 15733, 19001, 22751, 27028, 31879, 37353, 43501, 50376, 58033, 66529, 75923, 86276, 97651, 110113, 123729, 138568, 154701, 172201, 191143, 211604, 233663, 257401, 282901, 310248, 339529
OFFSET
1,2
FORMULA
a(n) = (n^4 + 8*n^3 + 11*n^2 - 20*n + 12)/12.
a(n) = [x^n] (-3*x^4 + 11*x^3 - 13*x^2 + 4*x - 1)/(x - 1)^5. - Peter Luschny, Apr 10 2023
EXAMPLE
The a(2) = 8 shapes are 211, 221, 222, 221/1, 222/1, 222/11, 221/11, 211/1.
MAPLE
a := proc(n) m := n*(n + 4); m*(m - 5) / 12 + 1 end:
seq(a(n), n = 1..43); # Peter Luschny, Apr 10 2023
CROSSREFS
Sequence in context: A288115 A100178 A106113 * A299260 A290312 A374974
KEYWORD
nonn,easy
AUTHOR
Richard Stanley, Apr 09 2023
STATUS
approved