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)}.

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

Offset: 1

Author

N. J. A. Sloane, Mar 31 2017

Keywords

• nonn
• tabl

Comments

A naive version of a two-dimensional 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.

T(n, 1) = T(n, n) = A000045(n) for n > 0. - Indranil Ghosh, Apr 01 2017

Examples

			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;
  ...
		

Links

• Indranil Ghosh, Rows 1..120, flattened
• Indranil Ghosh, C program to generate the triangle

Crossrefs

Cf. A000045, A058071.

Programs

Mathematica

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

PARI

tabl(nn) = {for(n=1, nn, for(m=1, n, print1(fibonacci(max(m, n - m + 1)),", ");); print(););}
tabl(20) \\ Indranil Ghosh, Apr 01 2017

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

Formula

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

Extensions

Extended by Indranil Ghosh, Apr 01 2017