A281450 -id:A281450 - cp's OEIS frontend

A045995 Rows of Fibonacci-Pascal triangle.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 8, 3, 1, 1, 5, 55, 55, 5, 1, 1, 8, 610, 6765, 610, 8, 1, 1, 13, 10946, 9227465, 9227465, 10946, 13, 1, 1, 21, 317811, 225851433717, 190392490709135, 225851433717, 317811, 21, 1, 1, 34, 14930352

Offset: 0

N. J. A. Sloane

			1,
1,  1,
1,  1,      1,
1,  2,      2,            1,
1,  3,      8,            3,               1,
1,  5,     55,           55,               5,            1,
1,  8,    610,         6765,             610,            8,      1,
1, 13,  10946,      9227465,         9227465,        10946,     13,  1,
1, 21, 317811, 225851433717, 190392490709135, 225851433717, 317811, 21, 1,
...

Reinhard Zumkeller, Rows n=0..14 of triangle, flattened
R. Whitney, Problem H-254, Fib. Quart., 13 (1975), p. 281.

Cf. A000045, A007318, A006449 (row sums), A081667.

Main diagonal gives A281450.

a045995 n k = a045995_tabl !! n !! k
a045995_row n = a045995_tabl !! n
a045995_tabl = map (map (a000045 . fromInteger)) a007318_tabl
-- Reinhard Zumkeller, Dec 29 2011

A045995 := proc(n,k)
    combinat[fibonacci](binomial(n,k)) ;
end proc: # R. J. Mathar, Dec 03 2014

Flatten[Table[Fibonacci[Binomial[n,k]],{n,0,10},{k,0,n}]] (* Harvey P. Dale, Dec 31 2013 *)

Take Pascal triangle (A007318) and replace each i by Fibonacci(i): a(n,k)=Fibonacci(binomial(n,k)).

More terms from David W. Wilson

A273397 a(n) = Fibonacci(Catalan(n)).

Original entry on oeis.org

1, 1, 1, 5, 377, 267914296, 1725375039079340637797070384, 202401005213503038261932567177107618332887918916819829782797456368284639448671475316218754

Offset: 0

Waldemar Puszkarz, May 21 2016

Next term, a(8), which has 299 digits, is too large to include. Counterpart to A273398.

The number of digits of a(n) grows faster than Fibonacci(n), in contrast to A273398, and faster than Catalan(n-2), but slower than Catalan(n-1) or Catalan(n).

			For n = 3, a(3) = Fibonacci(Catalan(3)) = Fibonacci(5) = 5.

Alois P. Heinz, Table of n, a(n) for n = 0..8

Cf. A000045 (Fibonacci), A000108(Catalan), A263986, A273398 (related sequences with Fibonacci and Catalan numbers), A281450.

a:= n-> (<<0|1>, <1|1>>^(binomial(2*n, n)/(n+1)))[1, 2]:
seq(a(n), n=0..8);  # Alois P. Heinz, Jan 20 2017

Mathematica
```
Fibonacci[CatalanNumber[Range[0, 7]]]
```

for(n=0,7, cn=binomial(2*n, n)/(n+1); print1(fibonacci(cn) ","))

a(n) = A000045(A000108(n)).

cp's OEIS Frontend

A045995 Rows of Fibonacci-Pascal triangle.

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