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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 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; MATHEMATICA T[n_, 1]:= Fibonacci[n]; T[n_, n_]:= Fibonacci[n]; T[n_, k_]:= T[n-1, k-1] + T[n-1, k]; Table[T[n, k], {n, 1, 12}, {k, 1, n}]//Flatten (* G. C. Greubel, Jul 12 2019 *) 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 (PARI) T(n, k) = if(k==1 || k==n, fibonacci(n), T(n-1, k-1) + T(n-1, k)); for(n=1, 12, for(k=1, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Jul 12 2019 (Sage) def T(n, k):     if (k==1 or k==n): return fibonacci(n)     else: return T(n-1, k-1) + T(n-1, k) [[T(n, k) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Jul 12 2019 (GAP) T:= function(n, k)     if k=1 then return Fibonacci(n);     elif k=n then return Fibonacci(n);     else return T(n-1, k-1) + T(n-1, k);     fi;   end; Flat(List([1..15], n-> List([1..n], k-> T(n, k) ))); # G. C. Greubel, Jul 12 2019 CROSSREFS Some other Fibonacci-Pascal triangles: A027926, A036355, A037027, A105809, A109906, A111006, A114197, A162741, A228074. Sequence in context: A051601 A296612 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

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Last modified April 11 22:31 EDT 2021. Contains 342895 sequences. (Running on oeis4.)