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A045995 Rows of Fibonacci-Pascal triangle.

%I A045995 #38 Jan 05 2025 19:51:35
%S A045995 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 A045995 13,10946,9227465,9227465,10946,13,1,1,21,317811,225851433717,
%U A045995 190392490709135,225851433717,317811,21,1,1,34,14930352
%N A045995 Rows of Fibonacci-Pascal triangle.
%H A045995 Reinhard Zumkeller, <a href="/A045995/b045995.txt">Rows n=0..14 of triangle, flattened</a>
%H A045995 R. Whitney, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/13-3/advanced13-3.pdf">Problem H-254</a>, Fib. Quart., 13 (1975), p. 281.
%F A045995 Take Pascal triangle (A007318) and replace each i by Fibonacci(i): a(n,k)=Fibonacci(binomial(n,k)).
%e A045995 1,
%e A045995 1,  1,
%e A045995 1,  1,      1,
%e A045995 1,  2,      2,            1,
%e A045995 1,  3,      8,            3,               1,
%e A045995 1,  5,     55,           55,               5,            1,
%e A045995 1,  8,    610,         6765,             610,            8,      1,
%e A045995 1, 13,  10946,      9227465,         9227465,        10946,     13,  1,
%e A045995 1, 21, 317811, 225851433717, 190392490709135, 225851433717, 317811, 21, 1,
%e A045995 ...
%p A045995 A045995 := proc(n,k)
%p A045995     combinat[fibonacci](binomial(n,k)) ;
%p A045995 end proc: # _R. J. Mathar_, Dec 03 2014
%t A045995 Flatten[Table[Fibonacci[Binomial[n,k]],{n,0,10},{k,0,n}]] (* _Harvey P. Dale_, Dec 31 2013 *)
%o A045995 (Haskell)
%o A045995 a045995 n k = a045995_tabl !! n !! k
%o A045995 a045995_row n = a045995_tabl !! n
%o A045995 a045995_tabl = map (map (a000045 . fromInteger)) a007318_tabl
%o A045995 -- _Reinhard Zumkeller_, Dec 29 2011
%Y A045995 Cf. A000045, A007318, A006449 (row sums), A081667.
%Y A045995 Main diagonal gives A281450.
%K A045995 nonn,easy,nice,tabl
%O A045995 0,8
%A A045995 _N. J. A. Sloane_
%E A045995 More terms from _David W. Wilson_