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Number of permutations of 1..n with displacements restricted to {-5,-4,0,1,2,3}
2

%I #5 Mar 31 2012 12:36:16

%S 1,1,1,1,8,35,107,247,535,1223,3009,8033,21789,56561,141754,352916,

%T 885060,2243639,5731032,14652087,37302363,94594125,239640285,

%U 607680601,1543064845,3921438808,9965699656,25314407628,64275368601,163181158704

%N Number of permutations of 1..n with displacements restricted to {-5,-4,0,1,2,3}

%H R. H. Hardin, <a href="/A189592/b189592.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = a(n-1) +3*a(n-3) +5*a(n-4) +9*a(n-5) +26*a(n-6) +63*a(n-7) +61*a(n-8) +4*a(n-9) -16*a(n-10) -125*a(n-11) -57*a(n-12) -33*a(n-13) -350*a(n-14) -394*a(n-15) -162*a(n-16) -303*a(n-17) +44*a(n-18) +67*a(n-19) -52*a(n-20) -96*a(n-21) +15*a(n-22) +285*a(n-23) -48*a(n-24) -49*a(n-25) +195*a(n-26) -485*a(n-27) +428*a(n-28) -165*a(n-29) +39*a(n-30) +88*a(n-31) -134*a(n-32) +111*a(n-33) +117*a(n-34) +96*a(n-35) +47*a(n-36) +26*a(n-37) +19*a(n-38) -2*a(n-39) +48*a(n-40) -26*a(n-41) +2*a(n-42) -43*a(n-43) +8*a(n-44) -36*a(n-45) +3*a(n-46) -a(n-47) -15*a(n-48) +6*a(n-49) -5*a(n-50) +4*a(n-51) -a(n-52) +2*a(n-53) +a(n-56)

%e Some solutions for n=9

%e ..6....5....6....6....1....5....5....6....5....6....6....5....1....6....1....1

%e ..1....1....2....2....2....1....1....2....1....1....1....7....2....1....2....7

%e ..8....7....1....3....8....2....8....1....2....3....3....2....7....2....8....8

%e ..3....2....8....1....9....3....4....4....8....9....8....1....9....8....4....2

%e ..2....9....4....9....5....9....2....9....3....2....2....4....4....3....3....3

%e ..5....3....3....4....3....4....3....3....4....5....4....3....3....4....5....4

%e ..4....4....7....7....4....6....7....5....7....4....7....6....6....7....6....6

%e ..7....8....5....5....6....7....6....7....6....7....5....8....5....5....7....5

%e ..9....6....9....8....7....8....9....8....9....8....9....9....8....9....9....9

%K nonn

%O 1,5

%A _R. H. Hardin_ Apr 24 2011