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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)}. 2

%I

%S 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 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 34,21,13,8,13,21,34,55,89,144,89,55,34,21,13,13,21,34,55,89,144

%N 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 A naive version of a two-dimensional Fibonacci array.

%C 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 See A058071 for a more interesting version.

%C T(n, 1) = T(n, n) = A000045(n) for n > 0. - _Indranil Ghosh_, Apr 01 2017

%H Indranil Ghosh, <a href="/A283845/b283845.txt">Rows 1..120, flattened</a>

%H Indranil Ghosh, <a href="/A283845/a283845_1.txt">C program to generate the triangle</a>

%F T(m,n) = Fibonacci(k) where k = max(m,n).

%e The square array begins:

%e 1, 1, 2, 3, 5, 8, 13, 21, ...

%e 1, 1, 2, 3, 5, 8, 13, 21, ...

%e 2, 2, 2, 3, 5, 8, 13, 21, ...

%e 3, 3, 3, 3, 5, 8, 13, 21, ...

%e 5, 5, 5, 5, 5, 8, 13, 21, ...

%e 8, 8, 8, 8, 8, 8, 13, 21, ...

%e 13, 13, 13, 13, 13, 13, 13, 21, ...

%e ...

%e The first few antidiagonals are:

%e 1;

%e 1, 1;

%e 2, 1, 2;

%e 3, 2, 2, 3;

%e 5, 3, 2, 3, 5;

%e 8, 5, 3, 3, 5, 8;

%e 13, 8, 5, 3, 5, 8, 13;

%e ...

%t Table[Fibonacci[Max[m, n - m + 1]], {n, 20}, {m, n}] // Flatten (* _Indranil Ghosh_, Apr 01 2017 *)

%o (PARI)

%o tabl(nn) = {for(n=1, nn, for(m=1, n, print1(fibonacci(max(m, n - m + 1)),", ");); print(););}

%o tabl(20) \\ _Indranil Ghosh_, Apr 01 2017

%o (Python)

%o from sympy import fibonacci

%o for n in xrange(1, 21):

%o ....print [fibonacci(max(m, n - m + 1)) for m in xrange(1, n + 1)] # _Indranil Ghosh_, Apr 01 2017

%Y Cf. A000045, A058071.

%K nonn,tabl

%O 1,4

%A _N. J. A. Sloane_, Mar 31 2017

%E Extended by _Indranil Ghosh_, Apr 01 2017

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Last modified April 18 14:39 EDT 2019. Contains 322209 sequences. (Running on oeis4.)