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A039913 Triangular "Fibonacci array".

%I A039913 #19 Jul 08 2025 22:40:38
%S A039913 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 A039913 18,19,19,18,21,13,21,34,29,31,30,31,29,34,21,34,55,47,50,49,49,50,47,
%U A039913 55,34,55,89,76,81,79,80,79,81,76,89,55,89,144,123,131,128,129,129,128
%N A039913 Triangular "Fibonacci array".
%C A039913 Sum of n-th row = 2*A001629(n+1). - _Reinhard Zumkeller_, Oct 07 2012
%H A039913 Reinhard Zumkeller, <a href="/A039913/b039913.txt">Rows n = 0..120 of triangle, flattened</a>
%H A039913 L. Carlitz, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/1-2/carlitz.pdf">A Fibonacci array</a>, Fib. Quart. 1(#2) (1963), 217-28.
%F A039913 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 A039913 G.f.: (x+y)/((1-x-x^2)*(1-y-y^2)). [U coordinates]
%e A039913 0;
%e A039913 1 1;
%e A039913 1 2 1;
%e A039913 2 3 3 2;
%e A039913 3 5 4 5 3;
%e A039913 ...
%o A039913 (Haskell)
%o A039913 a039913 n k = a039913_tabl !! n !! k
%o A039913 a039913_row n = a039913_tabl !! n
%o A039913 a039913_tabl = [[0], [1, 1]] ++ f [0] [1, 1] where
%o A039913    f us@(u:us') vs@(v:vs') = ws : f vs ws where
%o A039913      ws = [u + v, u + v + v] ++ zipWith (+) us vs'
%o A039913 -- _Reinhard Zumkeller_, Oct 07 2012
%Y A039913 Cf. A108035.
%K A039913 tabl,nonn,easy
%O A039913 0,5
%A A039913 _N. J. A. Sloane_
%E A039913 More terms from Larry Reeves (larryr(AT)acm.org), Sep 28 2000