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

0,8

Links

Reinhard Zumkeller, Rows n=0..14 of triangle, flattened

R. Whitney, Problem H-254, Fib. Quart., 13 (1975), p. 281.

Formula

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

Example

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,
...

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 *)

Prog

(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

Crossrefs

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

Main diagonal gives A281450.

Sequence in context: A379432 A331485 A342061 * A360625 A157654 A357437

Adjacent sequences: A045992 A045993 A045994 * A045996 A045997 A045998

Keyword

nonn,easy,nice,tabl

Author

N. J. A. Sloane

Extensions

More terms from David W. Wilson

Status

approved