A316938 - OEIS

%I #21 Sep 14 2021 01:04:33

%S 3,5,5,8,10,8,13,18,18,13,21,31,36,31,21,34,52,67,67,52,34,55,86,119,

%T 134,119,86,55,89,141,205,253,253,205,141,89,144,230,346,458,506,458,

%U 346,230,144,233,374,576,804,964,964,804,576,374,233,377,607,950,1380,1768,1928,1768,1380,950,607,377

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

%C Row sums give A316937.

%e Triangle begins:

%e     3;

%e     5,   5;

%e     8,  10,   8;

%e    13,  18,  18,  13;

%e    21,  31,  36,  31,  21;

%e    34,  52,  67,  67,  52,  34;

%e    55,  86, 119, 134, 119,  86,  55;

%e    89, 141, 205, 253, 253, 205, 141,  89;

%e   144, 230, 346, 458, 506, 458, 346, 230, 144;

%e ...

%t 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

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

%Y Other Fibonacci borders: A074829, A108617, A316939.

%K nonn,tabl

%O 0,1

%A _Vincenzo Librandi_, Jul 27 2018