A379837 Triangle read by rows formed using Pascal's rule except that n-th row begins and ends with Fibonacci(n+3).

2, 3, 3, 5, 6, 5, 8, 11, 11, 8, 13, 19, 22, 19, 13, 21, 32, 41, 41, 32, 21, 34, 53, 73, 82, 73, 53, 34, 55, 87, 126, 155, 155, 126, 87, 55, 89, 142, 213, 281, 310, 281, 213, 142, 89, 144, 231, 355, 494, 591, 591, 494, 355, 231, 144

Offset

0,1

Links

Table of n, a(n) for n=0..54.

Example

Triangle begins:
      k= 0   1   2  3    4   5   6
  n=0:   2;
  n=1:   3,  3;
  n=2:   5,  6,  5;
  n=3:   8, 11, 11, 8;
  n=4:  13, 19, 22, 19, 13;
  n=5:  21, 32, 41, 41, 32, 21;
  n=6:  34, 53, 73, 82, 73, 53, 34;
  ...

Mathematica

// As triangle // t={}; Do[r={}; Do[If[k==0||k==n, m=Fibonacci[n+3], m=t[[n, k]]+t[[n, k+1]]]; r=AppendTo[r, m], {k, 0, n}]; AppendTo[t, r], {n, 0, 11}]; t

Crossrefs

Cf. A000045, A074829, A316938, A316939.

Cf. A108617.

Sequence in context: A207292 A064464 A094585 * A183322 A295918 A296834

Adjacent sequences: A379833 A379834 A379835 * A379838 A379839 A379840

Keyword

nonn,tabl,new

Author

Vincenzo Librandi, Jan 26 2025

Status

approved