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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice
• tabl

Examples

			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,
...
		

Links

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

Crossrefs

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

Main diagonal gives A281450.

Programs

Haskell

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

Maple

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

Mathematica

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

Formula

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

Extensions

More terms from David W. Wilson