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

%I A379837 #11 Jan 26 2025 20:48:15
%S A379837 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,
%T A379837 73,53,34,55,87,126,155,155,126,87,55,89,142,213,281,310,281,213,142,
%U A379837 89,144,231,355,494,591,591,494,355,231,144
%N A379837 Triangle read by rows formed using Pascal's rule except that n-th row begins and ends with Fibonacci(n+3).
%e A379837 Triangle begins:
%e A379837       k= 0   1   2  3    4   5   6
%e A379837   n=0:   2;
%e A379837   n=1:   3,  3;
%e A379837   n=2:   5,  6,  5;
%e A379837   n=3:   8, 11, 11, 8;
%e A379837   n=4:  13, 19, 22, 19, 13;
%e A379837   n=5:  21, 32, 41, 41, 32, 21;
%e A379837   n=6:  34, 53, 73, 82, 73, 53, 34;
%e A379837   ...
%t A379837 // 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
%Y A379837 Cf. A000045, A074829, A316938, A316939.
%Y A379837 Cf. A108617.
%K A379837 nonn,tabl
%O A379837 0,1
%A A379837 _Vincenzo Librandi_, Jan 26 2025