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A074829 Triangle formed by Pascal's rule, except begin and end the n-th row with the n-th 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 (list; table; graph; refs; listen; history; text; internal format)
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 !! (n-1) !! (k-1)

a074829_row n = a074829_tabl !! (n-1)

a074829_tabl = map fst $ iterate

   (\(u:_, vs) -> (vs, zipWith (+) ([u] ++ vs) (vs ++ [u]))) ([1], [1, 1])

-- Reinhard Zumkeller, Aug 15 2013

CROSSREFS

Some other Fibonacci-Pascal triangles: A027926, A036355, A037027, A105809, A109906, A111006, A114197, A162741, A228074.

Sequence in context: A300401 A051601 A193921 * A060243 A054225 A228482

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

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Last modified October 21 13:03 EDT 2018. Contains 316422 sequences. (Running on oeis4.)