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A316939
Triangle read by rows formed using Pascal's rule except that n-th row begins and ends with Fibonacci(n+2).
3
1, 2, 2, 3, 4, 3, 5, 7, 7, 5, 8, 12, 14, 12, 8, 13, 20, 26, 26, 20, 13, 21, 33, 46, 52, 46, 33, 21, 34, 54, 79, 98, 98, 79, 54, 34, 55, 88, 133, 177, 196, 177, 133, 88, 55, 89, 143, 221, 310, 373, 373, 310, 221, 143, 89, 144, 232, 364, 531, 683, 746, 683, 531, 364, 232, 144, 233, 376, 596, 895, 1214, 1429
OFFSET
0,2
EXAMPLE
Triangle begins:
1;
2, 2;
3, 4, 3;
5, 7, 7, 5;
8, 12, 14, 12, 8;
13, 20, 26, 26, 20, 13;
21, 33, 46, 52, 46, 33, 21;
34, 54, 79, 98, 98, 79, 54, 34;
55, 88, 133, 177, 196, 177, 133, 88, 55;
...
MAPLE
f:= proc(n, k) option remember;
if k=0 or k=n then combinat:-fibonacci(n+2) else procname(n-1, k)+procname(n-1, k-1) fi
end proc:
for n from 0 to 10 do
seq(f(n, k), k=0..n)
od; # Robert Israel, Sep 20 2018
MATHEMATICA
t={}; Do[r={}; Do[If[k==0||k==n, m=Fibonacci[n + 2], m=t[[n, k]] + t[[n, k + 1]]]; r=AppendTo[r, m], {k, 0, n}]; AppendTo[t, r], {n, 0, 10}]; t // Flatten
CROSSREFS
Cf. A316528 (row sums).
Columns k=0..2: A000045, A000071, A001924.
Other Fibonacci borders: A074829, A108617, A316938.
Sequence in context: A143061 A096858 A037254 * A259478 A155706 A317533
KEYWORD
nonn,tabl
AUTHOR
Vincenzo Librandi, Jul 28 2018
EXTENSIONS
Incorrect g.f. removed by Georg Fischer, Feb 18 2020
STATUS
approved