A316939 Triangle read by rows formed using Pascal's rule except that n-th row begins and ends with Fibonacci(n+2).

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

Author

Vincenzo Librandi, Jul 28 2018

Keywords

• nonn
• tabl

Examples

			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;
  ...
		

Crossrefs

Cf. A316528 (row sums).

Columns k=0..2: A000045, A000071, A001924.

Other Fibonacci borders: A074829, A108617, A316938.

Programs

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

Extensions

Incorrect g.f. removed by Georg Fischer, Feb 18 2020