A316938 Triangle read by rows formed using Pascal's rule except that n-th row begins and ends with Fibonacci(n+4).

3, 5, 5, 8, 10, 8, 13, 18, 18, 13, 21, 31, 36, 31, 21, 34, 52, 67, 67, 52, 34, 55, 86, 119, 134, 119, 86, 55, 89, 141, 205, 253, 253, 205, 141, 89, 144, 230, 346, 458, 506, 458, 346, 230, 144, 233, 374, 576, 804, 964, 964, 804, 576, 374, 233, 377, 607, 950, 1380, 1768, 1928, 1768, 1380, 950, 607, 377

Offset

0,1

Comments

Row sums give A316937.

Links

Table of n, a(n) for n=0..65.

Example

Triangle begins:
    3;
    5,   5;
    8,  10,   8;
   13,  18,  18,  13;
   21,  31,  36,  31,  21;
   34,  52,  67,  67,  52,  34;
   55,  86, 119, 134, 119,  86,  55;
   89, 141, 205, 253, 253, 205, 141,  89;
  144, 230, 346, 458, 506, 458, 346, 230, 144;
...

Mathematica

t={}; Do[r={}; Do[If[k==0||k==n, m=Fibonacci[n+4], m=t[[n, k]]+t[[n, k+1]]]; r=AppendTo[r, m], {k, 0, n}]; AppendTo[t, r], {n, 0, 10}]; t

Crossrefs

Cf. A000045 (Fibonacci numbers), A316937 (row sums).

Other Fibonacci borders: A074829, A108617, A316939.

Sequence in context: A263209 A101330 A063285 * A112507 A229428 A348374

Adjacent sequences: A316935 A316936 A316937 * A316939 A316940 A316941

Keyword

nonn,tabl

Author

Vincenzo Librandi, Jul 27 2018

Status

approved