login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A307301 Array read by antidiagonals: Sprague-Grundy values for the game NimHof with rules [1,0], [3,1], [0,1]. 2
0, 1, 1, 2, 0, 2, 3, 3, 3, 3, 4, 2, 0, 2, 4, 5, 5, 4, 1, 5, 5, 6, 4, 1, 0, 6, 4, 6, 7, 7, 6, 6, 1, 7, 7, 7, 8, 6, 5, 7, 0, 6, 4, 6, 8, 9, 9, 8, 8, 2, 2, 8, 5, 9, 9, 10, 8, 7, 4, 3, 0, 3, 9, 10, 8, 10, 11, 11, 10, 5, 9, 9, 1, 8, 5, 11, 11, 11, 12, 10, 9, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The game NimHof with a list of rules R means that for each rule [a,b] you can move from cell [x,y] to any cell [x-i*a,y-i*b] as long as neither coordinate is negative. See the Friedman et al. article for further details.

REFERENCES

Eric Friedman, Scott M. Garrabrant, Ilona K. Phipps-Morgan, A. S. Landsberg and Urban Larsson, Geometric analysis of a generalized Wythoff game, in Games of no Chance 5, MSRI publ. Cambridge University Press, date?

LINKS

Table of n, a(n) for n=0..81.

Rémy Sigrist, Colored representation of T(x,y) for x = 0..1023 and y = 0..1023 (where the hue is function of T(x,y) and black pixels correspond to zeros)

Rémy Sigrist, PARI program for A307301

N. J. A. Sloane, Maple program for NimHof sequences

EXAMPLE

The initial antidiagonals are:

[0]

[1, 1]

[2, 0, 2]

[3, 3, 3, 3]

[4, 2, 0, 2, 4]

[5, 5, 4, 1, 5, 5]

[6, 4, 1, 0, 6, 4, 6]

[7, 7, 6, 6, 1, 7, 7, 7]

[8, 6, 5, 7, 0, 6, 4, 6, 8]

[9, 9, 8, 8, 2, 2, 8, 5, 9, 9]

[10, 8, 7, 4, 3, 0, 3, 9, 10, 8, 10]

[11, 11, 10, 5, 9, 9, 1, 8, 5, 11, 11, 11]

[12, 10, 9, 11, 10, 1, 0, 3, 7, 7, 8, 10, 12]

...

The triangle begins:

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]

[1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10]

[2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8]

[3, 2, 4, 0, 1, 6, 8, 9, 5, 7]

[4, 5, 1, 6, 0, 2, 3, 8, 7]

[5, 4, 6, 7, 2, 0, 1, 3]

[6, 7, 5, 8, 3, 9, 0]

[7, 6, 8, 4, 9, 1]

[8, 9, 7, 5, 10]

[9, 8, 10, 11]

[10, 11, 9]

[11, 10]

[12]

...

PROG

(PARI) See Links section.

CROSSREFS

Cf. A003987, A307296, A307297.

Sequence in context: A003987 A307302 A307297 * A307300 A141692 A261097

Adjacent sequences:  A307298 A307299 A307300 * A307302 A307303 A307304

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Apr 13 2019

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 July 26 01:49 EDT 2021. Contains 346294 sequences. (Running on oeis4.)