A350834 Number of ways to tile an n X n right triangle with squares and dominoes, where vertical dominoes are only allowed in the largest vertical column.
1, 1, 3, 11, 73, 749, 12657, 343693, 15140923, 1078147567, 124268659473, 23172219304577, 6991754237772409, 3413365649747365697, 2696315730346059254139, 3446235324323962173174283, 7127008624714819485698797681, 23848280807640171362927751869341
Offset: 0
Keywords
Examples
Here is one of the 73 tilings for the n=4 case. Note that vertical dominoes are only allowed in the "first" column. . _ | |_ |_|_|_ | |___|_ |_|_|___|
Programs
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Mathematica
T[0] = 1; T[1] = 1; T[n_] := T[n] = Fibonacci[n + 1] T[n - 1] + (Fibonacci[n] Fibonacci[n - 1]) T[n - 2]; Table[T[n], {n, 0, 20}]
Formula
a(n) = Fibonacci(n+1)*a(n-1) + Fibonacci(n)*Fibonacci(n-1)*a(n-2).
a(n) = P(n+1) + Sum_{i=2..n} a(i-1)*Fibonacci(i-1)*Fibonacci(n-(i-1))*P(n)/P(i), where P(n) = A003266(n) the product of the first n Fibonacci numbers. - Greg Dresden and Tianle Tina Yao, Jul 03 2022
Comments