A374980
Number of multiset permutations of {1, 1, 2, 2, ..., n, n} with no fixed pair (j,j).
Original entry on oeis.org
1, 0, 5, 74, 2193, 101644, 6840085, 630985830, 76484389121, 11792973495032, 2254432154097861, 523368281765512930, 145044815855963403985, 47302856057098946329284, 17933275902554972391519893, 7820842217155394547769452734, 3887745712142302082441578104705
Offset: 0
a(2) = 5: 1212, 1221, 2112, 2121, 2211.
-
a:= proc(n) option remember; `if`(n<3, [1, 0, 5][n+1],
(n-1)*((2*n+1)*a(n-1)+(4*n-3)*a(n-2)+2*(n-2)*a(n-3)))
end:
seq(a(n), n=0..16);
A375223
a(n) is the number of permutations of the multiset 1,1, 2,2, ..., n,n such that at least one pair k,k stays at its initial locations 2k-1, 2k.
Original entry on oeis.org
1, 1, 16, 327, 11756, 644315, 50094570, 5245258879, 711662648968, 121448713262139, 25460198594647070, 6431844723440756015, 1927058631207405670716, 675631849624828664480107, 274032655042818911590547266, 127312224468011793400981895295, 67167619760422081463964260973200
Offset: 1
a(3) = 16: The 15 permutations with one stable pair (see A375222) and the starting configuration [1, 1, 2, 2, 3, 3].
-
a375223(n) = {my (p=vector(2*n,i,1+(i-1)\2), m=0); forperm (p, q, for (j=1, n, if (q[2*j-1]==j && q[2*j]==j, m++; break))); m}
A375220
T(n,k) is the number of permutations of the multiset {1, 1, 2, 2, ..., n, n} with k occurrences of fixed pairs (j,j), where T(n,k), n >= 2, 0 <= k <= n-2 is a triangle read by rows.
Original entry on oeis.org
5, 74, 15, 2193, 296, 30, 101644, 10965, 740, 50, 6840085, 609864, 32895, 1480, 75, 630985830, 47880595, 2134524, 76755, 2590, 105, 76484389121, 5047886640, 191522380, 5692064, 153510, 4144, 140, 11792973495032, 688359502089, 22715489880, 574567140, 12807144, 276318, 6216, 180
Offset: 2
The triangle begins
5,
74, 15,
2193, 296, 30,
101644, 10965, 740, 50,
6840085, 609864, 32895, 1480, 75,
630985830, 47880595, 2134524, 76755, 2590, 105
Cf.
A375219 (similar for triples in the multiset).
Showing 1-3 of 3 results.
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