|
|
A274528
|
|
Square array read by antidiagonals upwards: T(n,k) = A269526(n+1,k+1) - 1, n>=0, k>=0.
|
|
25
|
|
|
0, 1, 2, 2, 3, 1, 3, 0, 4, 5, 4, 1, 5, 0, 3, 5, 6, 2, 1, 7, 4, 6, 7, 0, 4, 8, 2, 9, 7, 4, 8, 3, 0, 6, 5, 10, 8, 5, 3, 6, 1, 7, 4, 11, 12, 9, 10, 6, 2, 4, 5, 8, 3, 13, 7, 10, 11, 7, 8, 5, 9, 2, 6, 14, 15, 13, 11, 8, 12, 9, 10, 13, 3, 14, 15, 16, 6, 17, 12, 9, 13, 10, 2, 3, 7, 15, 8, 5, 11, 14, 6
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
This sequence has essentially the same properties as the main sequence A269526, but now involves the nonnegative integers.
Sprague-Grundy (Nim) values for a combinatorial game played with two piles of counters. Legal moves consist of removing any positive number of counters from either pile, or removing the same number from both piles, or moving any positive number of counters from the right pile to the left pile. If the Nim-values (as in Sprague-Grundy theory) are written in an array indexed by the number of counters in the two piles, we obtain this array. - Allan C. Wechsler, Jun 29 2016 [corrected by N. J. A. Sloane, Sep 25 2016]
The same sequence arises if we construct a triangle, by reading from left to right in each row, always choosing the smallest nonnegative number which does not produce a duplicate number in any row or diagonal. - N. J. A. Sloane, Jul 02 2016
It appears that the numbers generally appear for the first time in or near the first few rows. - Omar E. Pol, Jul 03 2016
|
|
LINKS
|
|
|
EXAMPLE
|
The corner of the square array begins:
0, 2, 1, 5, 3, 4, 9, 10, 12, 7, 13, 17,
1, 3, 4, 0, 7, 2, 5, 11, 13, 15, 6,
2, 0, 5, 1, 8, 6, 4, 3, 14, 16,
3, 1, 2, 4, 0, 7, 8, 6, 15,
4, 6, 0, 3, 1, 5, 2, 14,
5, 7, 8, 6, 4, 9, 3,
6, 4, 3, 2, 5, 13,
7, 5, 6, 8, 10,
8, 10, 7, 9,
9, 11, 12,
10, 8,
11,
|
|
MAPLE
|
A:= proc(n, k) option remember; local m, s;
if n=1 and k=1 then 0
else s:= {seq(A(i, k), i=1..n-1),
seq(A(n, j), j=1..k-1),
seq(A(n-t, k-t), t=1..min(n, k)-1),
seq(A(n+j, k-j), j=1..k-1)};
for m from 0 while m in s do od; m
fi
end:
[seq(seq(A(1+d-k, k), k=1..d), d=1..12)];
|
|
MATHEMATICA
|
A[n_, k_] := A[n, k] = Module[{m, s}, If[n==1 && k==1, 0, s = Join[Table[ A[i, k], {i, 1, n-1}], Table[A[n, j], {j, 1, k-1}], Table[A[n-t, k-t], {t, 1, Min[n, k] - 1}], Table[A[n+j, k-j], {j, 1, k-1}]]; For[m = 0, MemberQ[s, m], m++]; m]];
Table[A[d-k+1, k], {d, 1, 13}, {k, 1, d}] // Flatten (* Jean-François Alcover, May 03 2019, from Maple *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|