A362190 Triangle read by rows: T(n,k) is the smallest integer not already in the same row or column and also not diagonally adjacent to an equal integer.

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

Offset: 1

Author

Gavin Lupo, Apr 10 2023

Keywords

• nonn
• easy
• tabl

Comments

This sequence is A025581 without diagonal adjacent restriction.

Examples

			Triangle begins:
  n\k|  1  2  3  4  5  6  7  8 ...
  ---+----------------------------
   1 |  0
   2 |  1  2
   3 |  3  0  1
   4 |  2  4  3  0
   5 |  5  1  2  4  3
   6 |  4  3  0  1  2  5
   7 |  6  5  4  3  0  1  2
   8 |  7  8  6  2  4  3  0  1
		

Links

• Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A025581.

Programs

PARI

\\ here f(S) gives smallest not in set S.
f(S)={for(k=0, oo, if(!setsearch(S,k), return(k)))}
T(n)={my(M=matrix(n,n)); for(i=2, n, for(j=1, i, my(S=Set(concat([M[j..i-1,j]~, M[i,1..j-1], M[i-1,max(1,j-1)], M[i-1,min(j+1,i-1)]]))); M[i,j]=f(S))); M}
{ my(A=T(10)); for(i=1, #A, print(A[i, 1..i])) } \\ Andrew Howroyd, Apr 10 2023