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A039913
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Triangular "Fibonacci array".
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5
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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)
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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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]
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EXAMPLE
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0;
1 1;
1 2 1;
2 3 3 2;
3 5 4 5 3;
...
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PROG
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(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'
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Sep 28 2000
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STATUS
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approved
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