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A039913 Triangular "Fibonacci array". 5
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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

LINKS

Reinhard Zumkeller, Rows n = 0..120 of triangle, flattened

L. Carlitz, A Fibonacci array, Fib. Quart. 1(#2) (1963), 217-28.

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]

EXAMPLE

0;

1 1;

1 2 1;

2 3 3 2;

3 5 4 5 3;

...

PROG

(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

CROSSREFS

Cf. A108035.

Sequence in context: A033767 A033775 A033791 * A108617 A092683 A172089

Adjacent sequences:  A039910 A039911 A039912 * A039914 A039915 A039916

KEYWORD

tabl,nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

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

STATUS

approved

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Last modified September 27 15:29 EDT 2020. Contains 337383 sequences. (Running on oeis4.)