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%I #22 Nov 17 2020 11:05:43
%S 1,1,1,1,2,0,1,3,2,0,1,4,6,4,2,1,5,12,18,20,14,1,6,20,48,90,124,90,1,
%T 7,30,100,272,582,860,646,1,8,42,180,650,1928,4386,6748,5242,1,9,56,
%U 294,1332,5110,15912,37566,59612,47622,1,10,72,448,2450,11604,46250,148648,360642,586540,479306
%N Triangle read by rows: T(n,k) is the number of permutations of k elements from [1..n] without consecutive adjacent values.
%e n\k 0 1 2 3 4 5 6 7 8
%e 0 1
%e 1 1 1
%e 2 1 2 0
%e 3 1 3 2 0
%e 4 1 4 6 4 2
%e 5 1 5 12 18 20 14
%e 6 1 6 20 48 90 124 90
%e 7 1 7 30 100 272 582 860 646
%e 8 1 8 42 180 650 1928 4386 6748 5242
%o (PARI) isok(s, p) = {for (i=1, #s-1, if (abs(s[p[i+1]] - s[p[i]]) == 1, return (0));); return (1);}
%o T(n, k) = {my(nb = 0); forsubset([n, k], s, for(i=1, k!, if (isok(s, numtoperm(k, i)), nb++););); nb;} \\ _Michel Marcus_, Nov 17 2020
%Y Diagonal is A002464.
%K nonn,tabl
%O 0,5
%A _Xiangyu Chen_, Nov 07 2020
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