

A074829


Triangle formed by Pascal's rule, except begin and end the nth row with the nth Fibonacci number.


14



1, 1, 1, 2, 2, 2, 3, 4, 4, 3, 5, 7, 8, 7, 5, 8, 12, 15, 15, 12, 8, 13, 20, 27, 30, 27, 20, 13, 21, 33, 47, 57, 57, 47, 33, 21, 34, 54, 80, 104, 114, 104, 80, 54, 34, 55, 88, 134, 184, 218, 218, 184, 134, 88, 55, 89, 143, 222, 318, 402, 436, 402, 318, 222
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OFFSET

1,4


LINKS

Reinhard Zumkeller, Rows n = 1..120 of table, flattened
Index entries for triangles and arrays related to Pascal's triangle


EXAMPLE

The first and second Fibonacci numbers are 1, 1, so the first and second rows of the triangle are 1; 1 1; respectively. The third row of the triangle begins and ends with the third Fibonacci number, 2 and the middle term is the sum of the contiguous two terms in the second row, i.e. 1 + 1 = 2; so the third row is 2 2 2.
Triangle begins:
1;
1, 1;
2, 2, 2;
3, 4, 4, 3;
5, 7, 8, 7, 5;
8, 12, 15, 15, 12, 8;
13, 20, 27, 30, 27, 20, 13;
21, 33, 47, 57, 57, 47, 33, 21;
34, 54, 80, 104, 114, 104, 80, 54, 34;


PROG

(Haskell)
a074829 n k = a074829_tabl !! (n1) !! (k1)
a074829_row n = a074829_tabl !! (n1)
a074829_tabl = map fst $ iterate
(\(u:_, vs) > (vs, zipWith (+) ([u] ++ vs) (vs ++ [u]))) ([1], [1, 1])
 Reinhard Zumkeller, Aug 15 2013


CROSSREFS

Some other FibonacciPascal triangles: A027926, A036355, A037027, A105809, A109906, A111006, A114197, A162741, A228074.
Sequence in context: A300401 A051601 A193921 * A060243 A054225 A322210
Adjacent sequences: A074826 A074827 A074828 * A074830 A074831 A074832


KEYWORD

easy,nonn,tabl


AUTHOR

Joseph L. Pe, Sep 30 2002


EXTENSIONS

More terms from Philippe Deléham, Sep 20 2006
Data error in 7th row fixed by Reinhard Zumkeller, Aug 15 2013


STATUS

approved



