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Triangular "Fibonacci array".
5

%I #15 Sep 07 2017 14:16:36

%S 0,1,1,1,2,1,2,3,3,2,3,5,4,5,3,5,8,7,7,8,5,8,13,11,12,11,13,8,13,21,

%T 18,19,19,18,21,13,21,34,29,31,30,31,29,34,21,34,55,47,50,49,49,50,47,

%U 55,34,55,89,76,81,79,80,79,81,76,89,55,89,144,123,131,128,129,129,128

%N Triangular "Fibonacci array".

%C Sum of n-th row = 2*A001629(n+1). - _Reinhard Zumkeller_, Oct 07 2012

%H Reinhard Zumkeller, <a href="/A039913/b039913.txt">Rows n = 0..120 of triangle, flattened</a>

%H L. Carlitz, <a href="http://www.fq.math.ca/Scanned/1-2/carlitz.pdf">A Fibonacci array</a>, Fib. Quart. 1(#2) (1963), 217-28.

%F a(0, n)=Fib(n), a(1, n)=Fib(n+2), a(r, n)=a(r-1, n)+a(r-2, n), r >= 2.

%F G.f.: (x+y)/((1-x-x^2)*(1-y-y^2)). [U coordinates]

%e 0;

%e 1 1;

%e 1 2 1;

%e 2 3 3 2;

%e 3 5 4 5 3;

%e ...

%o (Haskell)

%o a039913 n k = a039913_tabl !! n !! k

%o a039913_row n = a039913_tabl !! n

%o a039913_tabl = [[0], [1, 1]] ++ f [0] [1, 1] where

%o f us@(u:us') vs@(v:vs') = ws : f vs ws where

%o ws = [u + v, u + v + v] ++ zipWith (+) us vs'

%o -- _Reinhard Zumkeller_, Oct 07 2012

%Y Cf. A108035.

%K tabl,nonn,easy

%O 0,5

%A _N. J. A. Sloane_.

%E More terms from Larry Reeves (larryr(AT)acm.org), Sep 28 2000