A362153 Number of skew shapes in a 3 X n rectangle with no empty rows or columns.

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

Links

Table of n, a(n) for n=1..43.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

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

Adjacent sequences: A362150 A362151 A362152 * A362154 A362155 A362156

Keyword

nonn,easy

Author

Richard Stanley, Apr 09 2023

Status

approved