A350834 - OEIS

%I #63 Jul 07 2022 16:35:40

%S 1,1,3,11,73,749,12657,343693,15140923,1078147567,124268659473,

%T 23172219304577,6991754237772409,3413365649747365697,

%U 2696315730346059254139,3446235324323962173174283,7127008624714819485698797681,23848280807640171362927751869341

%N 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.

%C This is the third column in A229556.

%F a(n) = Fibonacci(n+1)*a(n-1) + Fibonacci(n)*Fibonacci(n-1)*a(n-2).

%F 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

%e Here is one of the 73 tilings for the n=4 case. Note that vertical dominoes are only allowed in the "first" column.

%e .  _

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%t 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}]

%Y Cf. A229556, A000045, A003266.

%K nonn

%O 0,3

%A _Greg Dresden_ and _Tianle Tina Yao_, Jun 12 2022