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

%I A316938 #21 Sep 14 2021 01:04:33
%S A316938 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 A316938 134,119,86,55,89,141,205,253,253,205,141,89,144,230,346,458,506,458,
%U A316938 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 A316938 Triangle read by rows formed using Pascal's rule except that n-th row begins and ends with Fibonacci(n+4).
%C A316938 Row sums give A316937.
%e A316938 Triangle begins:
%e A316938     3;
%e A316938     5,   5;
%e A316938     8,  10,   8;
%e A316938    13,  18,  18,  13;
%e A316938    21,  31,  36,  31,  21;
%e A316938    34,  52,  67,  67,  52,  34;
%e A316938    55,  86, 119, 134, 119,  86,  55;
%e A316938    89, 141, 205, 253, 253, 205, 141,  89;
%e A316938   144, 230, 346, 458, 506, 458, 346, 230, 144;
%e A316938 ...
%t A316938 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 A316938 Cf. A000045 (Fibonacci numbers), A316937 (row sums).
%Y A316938 Other Fibonacci borders: A074829, A108617, A316939.
%K A316938 nonn,tabl
%O A316938 0,1
%A A316938 _Vincenzo Librandi_, Jul 27 2018