login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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

LINKS

Indranil Ghosh, Rows 1..120, flattened

Indranil Ghosh, C program to generate the triangle

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(); ); }

tabl(20) \\ Indranil Ghosh, Apr 01 2017

(Python)

from sympy import fibonacci

for n in xrange(1, 21):

....print [fibonacci(max(m, n - m + 1)) for m in xrange(1, n + 1)] # Indranil Ghosh, Apr 01 2017

CROSSREFS

Cf. A000045, A058071.

Sequence in context: A003984 A087061 A082860 * A058071 A174961 A104889

Adjacent sequences:  A283842 A283843 A283844 * A283846 A283847 A283848

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Mar 31 2017

EXTENSIONS

Extended by Indranil Ghosh, Apr 01 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 26 04:32 EDT 2019. Contains 321481 sequences. (Running on oeis4.)