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A283845 Square array read by antidiagonals: T(1,1) = T(1,2) = T(2,1) = T(2,2) = 1; thereafter T(m,n) = min {T(m,n-2) + T(m,n-1), T(m-2,n) + T(m-1,n), T(m-2,n-2) + T(m-1,n-1)}.

%I A283845 #35 Jun 13 2025 22:43:57
%S A283845 1,1,1,2,1,2,3,2,2,3,5,3,2,3,5,8,5,3,3,5,8,13,8,5,3,5,8,13,21,13,8,5,
%T A283845 5,8,13,21,34,21,13,8,5,8,13,21,34,55,34,21,13,8,8,13,21,34,55,89,55,
%U A283845 34,21,13,8,13,21,34,55,89,144,89,55,34,21,13,13,21,34,55,89,144
%N A283845 Square array read by antidiagonals: T(1,1) = T(1,2) = T(2,1) = T(2,2) = 1; thereafter T(m,n) = min {T(m,n-2) + T(m,n-1), T(m-2,n) + T(m-1,n), T(m-2,n-2) + T(m-1,n-1)}.
%C A283845 A naive version of a two-dimensional Fibonacci array.
%C A283845 There should probably be another entry for the array which has offset 0 and starts with T(0,0) = 0, T(0,1) = T(1,0) = T(1,1) = 1.
%C A283845 See A058071 for a more interesting version.
%C A283845 T(n, 1) = T(n, n) = A000045(n) for n > 0. - _Indranil Ghosh_, Apr 01 2017
%H A283845 Indranil Ghosh, <a href="/A283845/b283845.txt">Rows 1..120, flattened</a>
%H A283845 Indranil Ghosh, <a href="/A283845/a283845_1.txt">C program to generate the triangle</a>
%F A283845 T(m,n) = Fibonacci(k) where k = max(m,n).
%e A283845 The square array begins:
%e A283845    1,  1,  2,  3,  5,  8, 13, 21, ...
%e A283845    1,  1,  2,  3,  5,  8, 13, 21, ...
%e A283845    2,  2,  2,  3,  5,  8, 13, 21, ...
%e A283845    3,  3,  3,  3,  5,  8, 13, 21, ...
%e A283845    5,  5,  5,  5,  5,  8, 13, 21, ...
%e A283845    8,  8,  8,  8,  8,  8, 13, 21, ...
%e A283845   13, 13, 13, 13, 13, 13, 13, 21, ...
%e A283845   ...
%e A283845 The first few antidiagonals are:
%e A283845    1;
%e A283845    1, 1;
%e A283845    2, 1, 2;
%e A283845    3, 2, 2, 3;
%e A283845    5, 3, 2, 3, 5;
%e A283845    8, 5, 3, 3, 5, 8;
%e A283845   13, 8, 5, 3, 5, 8, 13;
%e A283845   ...
%t A283845 Table[Fibonacci[Max[m, n - m + 1]], {n, 20}, {m, n}] // Flatten (* _Indranil Ghosh_, Apr 01 2017 *)
%o A283845 (PARI)
%o A283845 tabl(nn) = {for(n=1, nn, for(m=1, n, print1(fibonacci(max(m, n - m + 1)),", ");); print(););}
%o A283845 tabl(20) \\ _Indranil Ghosh_, Apr 01 2017
%o A283845 (Python)
%o A283845 from sympy import fibonacci
%o A283845 for n in range(1, 21):
%o A283845     print([fibonacci(max(m, n - m + 1)) for m in range(1, n + 1)]) # _Indranil Ghosh_, Apr 01 2017
%Y A283845 Cf. A000045, A058071.
%K A283845 nonn,tabl
%O A283845 1,4
%A A283845 _N. J. A. Sloane_, Mar 31 2017
%E A283845 Extended by _Indranil Ghosh_, Apr 01 2017