A045995 - OEIS

%I #36 Jan 10 2018 10:33:11

%S 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,

%T 13,10946,9227465,9227465,10946,13,1,1,21,317811,225851433717,

%U 190392490709135,225851433717,317811,21,1,1,34,14930352

%N Rows of Fibonacci-Pascal triangle.

%H Reinhard Zumkeller, <a href="/A045995/b045995.txt">Rows n=0..14 of triangle, flattened</a>

%H R. Whitney, <a href="http://www.fq.math.ca/Scanned/13-3/advanced13-3.pdf">Problem H-254</a>, Fib. Quart., 13 (1975), p. 281.

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

%e 1,

%e 1,  1,

%e 1,  1,      1,

%e 1,  2,      2,            1,

%e 1,  3,      8,            3,               1,

%e 1,  5,     55,           55,               5,            1,

%e 1,  8,    610,         6765,             610,            8,      1,

%e 1, 13,  10946,      9227465,         9227465,        10946,     13,  1,

%e 1, 21, 317811, 225851433717, 190392490709135, 225851433717, 317811, 21, 1,

%e ...

%p A045995 := proc(n,k)

%p     combinat[fibonacci](binomial(n,k)) ;

%p end proc: # _R. J. Mathar_, Dec 03 2014

%t Flatten[Table[Fibonacci[Binomial[n,k]],{n,0,10},{k,0,n}]] (* _Harvey P. Dale_, Dec 31 2013 *)

%o (Haskell)

%o a045995 n k = a045995_tabl !! n !! k

%o a045995_row n = a045995_tabl !! n

%o a045995_tabl = map (map (a000045 . fromInteger)) a007318_tabl

%o -- _Reinhard Zumkeller_, Dec 29 2011

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

%Y Main diagonal gives A281450.

%K nonn,easy,nice,tabl

%O 0,8

%A _N. J. A. Sloane_

%E More terms from _David W. Wilson_