

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,n2) + T(m,n1), T(m2,n) + T(m1,n), T(m2,n2) + T(m1,n1)}.


2



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, 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, 34, 21, 13, 8, 13, 21, 34, 55, 89, 144, 89, 55, 34, 21, 13, 13, 21, 34, 55, 89, 144
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OFFSET

1,4


COMMENTS

A naive version of a twodimensional Fibonacci array.
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.
See A058071 for a more interesting version.


LINKS



FORMULA

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


EXAMPLE

The square array begins:
1, 1, 2, 3, 5, 8, 13, 21, ...
1, 1, 2, 3, 5, 8, 13, 21, ...
2, 2, 2, 3, 5, 8, 13, 21, ...
3, 3, 3, 3, 5, 8, 13, 21, ...
5, 5, 5, 5, 5, 8, 13, 21, ...
8, 8, 8, 8, 8, 8, 13, 21, ...
13, 13, 13, 13, 13, 13, 13, 21, ...
...
The first few antidiagonals are:
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;
...


MATHEMATICA

Table[Fibonacci[Max[m, n  m + 1]], {n, 20}, {m, n}] // Flatten (* Indranil Ghosh, Apr 01 2017 *)


PROG

(PARI)
tabl(nn) = {for(n=1, nn, for(m=1, n, print1(fibonacci(max(m, n  m + 1)), ", "); ); print(); ); }
(Python)
from sympy import fibonacci
for n in range(1, 21):
....print [fibonacci(max(m, n  m + 1)) for m in range(1, n + 1)] # Indranil Ghosh, Apr 01 2017


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



