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

Author

Richard Stanley, Apr 09 2023

Keywords

• nonn
• easy

Examples

			The a(2) = 8 shapes are 211, 221, 222, 221/1, 222/1, 222/11, 221/11, 211/1.
		

Links

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

Programs

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

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