A039913 Triangular "Fibonacci array".

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, 18, 19, 19, 18, 21, 13, 21, 34, 29, 31, 30, 31, 29, 34, 21, 34, 55, 47, 50, 49, 49, 50, 47, 55, 34, 55, 89, 76, 81, 79, 80, 79, 81, 76, 89, 55, 89, 144, 123, 131, 128, 129, 129, 128

Offset: 0

Author

N. J. A. Sloane

Keywords

• tabl
• nonn
• easy

Comments

Sum of n-th row = 2*A001629(n+1). - Reinhard Zumkeller, Oct 07 2012

Examples

			0;
1 1;
1 2 1;
2 3 3 2;
3 5 4 5 3;
...
		

Links

• Reinhard Zumkeller, Rows n = 0..120 of triangle, flattened
• L. Carlitz, A Fibonacci array, Fib. Quart. 1(#2) (1963), 217-28.

Crossrefs

Cf. A108035.

Programs

Haskell

a039913 n k = a039913_tabl !! n !! k
a039913_row n = a039913_tabl !! n
a039913_tabl = [[0], [1, 1]] ++ f [0] [1, 1] where
   f us@(u:us') vs@(v:vs') = ws : f vs ws where
     ws = [u + v, u + v + v] ++ zipWith (+) us vs'
-- Reinhard Zumkeller, Oct 07 2012

Formula

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

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

Extensions

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