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 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, 1, 3, 11, 73, 749, 12657, 343693, 15140923, 1078147567, 124268659473, 23172219304577, 6991754237772409, 3413365649747365697, 2696315730346059254139, 3446235324323962173174283, 7127008624714819485698797681, 23848280807640171362927751869341 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This is the third column in A229556. LINKS Table of n, a(n) for n=0..17. 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 EXAMPLE Here is one of the 73 tilings for the n=4 case. Note that vertical dominoes are only allowed in the "first" column. . _ | |_ |_|_|_ | |___|_ |_|_|___| 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}] CROSSREFS Cf. A229556, A000045, A003266. Sequence in context: A127716 A035378 A258387 * A054461 A342433 A203772 Adjacent sequences: A350831 A350832 A350833 * A350835 A350836 A350837 KEYWORD nonn AUTHOR Greg Dresden and Tianle Tina Yao, Jun 12 2022 STATUS approved

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)