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A220641 Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly one king-move neighbor. 2

%I #10 Nov 03 2023 15:42:29

%S 1,8,728,37320,2226936,128171936,7444342896,431408410784,

%T 25014514225856,1450226501771584,84080327982982848,

%U 4874715696405194752,282621433306639435392,16385536749696632356608,949984033027704106955264,55077209132605857634211328

%N Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly one king-move neighbor.

%C Column 5 of A220644.

%H Alois P. Heinz, <a href="/A220641/b220641.txt">Table of n, a(n) for n = 0..300</a> (terms n = 1..210 from R. H. Hardin)

%F Empirical: a(n) = 48*a(n-1) +694*a(n-2) -6232*a(n-3) -31552*a(n-4) +254384*a(n-5) +127448*a(n-6) -2270720*a(n-7) +175600*a(n-8) +6932672*a(n-9) -38400*a(n-10) -7223680*a(n-11) -640000*a(n-12) +1681408*a(n-13) +237568*a(n-14) +192512*a(n-15) -16384*a(n-16) +32768*a(n-17).

%F G.f.: see Maple program. - _Alois P. Heinz_, Jun 03 2014

%e Some solutions for n=3 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10)

%e ..0..6..4..9..0....6..4..0..0..7....0..9..0..6..4....0..7..6..4..0

%e ..6..4..0..8..1....0..7..7..3..0....0..7..1..0..0....3..9..0..9..0

%e ..0..0..0..2..0....3..3..0..0..0....3..0..0..6..4....0..0..1..0..1

%p gf:= -(4096*x^15 -4096*x^14 +31232*x^13 +42240*x^12 +242304*x^11 -32896*x^10 -801152*x^9 -74640*x^8 +473568*x^7 -18040*x^6 -86144*x^5 +11752*x^4 +3056*x^3 -350*x^2 -40*x+1) / (32768*x^17 -16384*x^16 +192512*x^15 +237568*x^14 +1681408*x^13 -640000*x^12 -7223680*x^11 -38400*x^10 +6932672*x^9 +175600*x^8 -2270720*x^7 +127448*x^6 +254384*x^5 -31552*x^4 -6232*x^3 +694*x^2 +48*x-1):

%p a:= n-> coeff(series(gf, x, n+1), x, n):

%p seq(a(n), n=0..25); # _Alois P. Heinz_, Jun 03 2014

%K nonn

%O 0,2

%A _R. H. Hardin_, Dec 17 2012

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)