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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.

%I A362190 #15 May 08 2023 02:28:39
%S A362190 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,
%T A362190 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,
%U A362190 11,9,10,5,7,6,8,4,3,0,1,2
%N 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.
%C A362190 This sequence is A025581 without diagonal adjacent restriction.
%H A362190 Neal Gersh Tolunsky, <a href="/A362190/b362190.txt">Table of n, a(n) for n = 1..10000</a>
%e A362190 Triangle begins:
%e A362190   n\k|  1  2  3  4  5  6  7  8 ...
%e A362190   ---+----------------------------
%e A362190    1 |  0
%e A362190    2 |  1  2
%e A362190    3 |  3  0  1
%e A362190    4 |  2  4  3  0
%e A362190    5 |  5  1  2  4  3
%e A362190    6 |  4  3  0  1  2  5
%e A362190    7 |  6  5  4  3  0  1  2
%e A362190    8 |  7  8  6  2  4  3  0  1
%o A362190 (PARI) \\ here f(S) gives smallest not in set S.
%o A362190 f(S)={for(k=0, oo, if(!setsearch(S,k), return(k)))}
%o A362190 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}
%o A362190 { my(A=T(10)); for(i=1, #A, print(A[i, 1..i])) } \\ _Andrew Howroyd_, Apr 10 2023
%Y A362190 Cf. A025581.
%K A362190 nonn,easy,tabl
%O A362190 1,3
%A A362190 _Gavin Lupo_, Apr 10 2023