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%I #20 Nov 24 2018 10:27:01
%S 1,0,1,1198,5609649,66218360625,1681287695542855,81644850343968535401,
%T 6945222145021508480249929,967335448974819561548523580438,
%U 209141786137614009701487336108267723
%N Number of permutations of 5 copies of 1..n introduced in order 1..n with no element equal to another within a distance of 1.
%H Seiichi Manyama, <a href="/A190833/b190833.txt">Table of n, a(n) for n = 0..100</a> (terms 1..17 from R. J. Mathar)
%H R. J. Mathar, <a href="http://vixra.org/abs/1511.0015">A class of multinomial permutations avoiding object clusters</a>, vixra:1511.0015 (2015)
%F From _Vaclav Kotesovec_, Nov 24 2018: (Start)
%F Recurrence: 72*(2562500*n^6 - 28700000*n^5 + 132339375*n^4 - 325827750*n^3 + 454176325*n^2 - 335170330*n + 94842168)*a(n) = 3*(1601562500*n^10 - 21140625000*n^9 + 123391796875*n^8 - 423007187500*n^7 + 944775218750*n^6 - 1434958662500*n^5 + 1501190434375*n^4 - 1066734651000*n^3 + 489294264300*n^2 - 138373925520*n + 5253272832)*a(n-1) + 40*(2946875000*n^9 - 37425312500*n^8 + 202210281250*n^7 - 613007709375*n^6 + 1158238267500*n^5 - 1429774838250*n^4 + 1130386059700*n^3 - 439029380875*n^2 - 90639409450*n + 124751567448)*a(n-2) - 1440*(166562500*n^8 - 1865500000*n^7 + 8477778125*n^6 - 20572469375*n^5 + 30057234250*n^4 - 27819019325*n^3 + 13875953795*n^2 + 328927290*n - 3329053712)*a(n-3) - 5760*(15375000*n^7 - 133762500*n^6 + 442461250*n^5 - 764293375*n^4 + 806629450*n^3 - 482585405*n^2 + 27997588*n + 122388456)*a(n-4) + 6912*(2562500*n^6 - 13325000*n^5 + 27276875*n^4 - 32220250*n^3 + 22166825*n^2 - 3068430*n - 5777712)*a(n-5).
%F a(n) ~ 5^(4*n + 1/2) * n^(4*n) / (24^n * exp(4*n + 4)). (End)
%e Some solutions for n=3
%e ..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
%e ..2....2....2....2....2....2....2....2....2....2....2....2....2....2....2....2
%e ..3....1....3....3....3....3....3....3....3....3....1....1....3....3....1....3
%e ..2....2....2....2....1....2....2....2....1....1....2....3....2....2....3....2
%e ..3....3....3....3....2....1....3....1....2....3....3....2....1....1....2....3
%e ..1....2....1....2....3....2....1....3....3....1....1....1....3....2....3....2
%e ..2....3....3....3....1....3....3....2....2....3....2....3....1....1....1....1
%e ..1....1....1....1....3....1....1....3....1....2....3....2....3....3....2....2
%e ..3....2....2....3....2....3....3....2....3....3....2....3....2....2....3....3
%e ..1....3....1....1....3....1....2....3....2....1....3....1....3....1....1....1
%e ..3....1....3....2....2....2....3....1....3....2....1....3....2....3....2....2
%e ..1....3....2....1....3....3....2....3....1....3....3....2....1....2....3....3
%e ..2....2....1....2....1....1....1....1....2....2....1....3....3....3....1....1
%e ..3....1....2....1....2....2....2....2....1....1....3....2....2....1....2....3
%e ..2....3....3....3....1....3....1....1....3....2....2....1....1....3....3....1
%K nonn
%O 0,4
%A _R. H. Hardin_ May 21 2011
%E a(0)=1 prepended by _Seiichi Manyama_, Nov 16 2018
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