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A220640 Number of ways to reciprocally link elements of an n X 4 array either to themselves or to exactly one king-move neighbor.

%I A220640 #12 Nov 03 2023 15:41:06
%S A220640 1,5,172,3755,92801,2226936,53841725,1299348473,31371388772,
%T A220640 757341382671,18283618480037,441397115736816,10656083384666537,
%U A220640 257256013409077661,6210599281867691164,149934463555725516099,3619673802389322978937,87385102146053809399912
%N A220640 Number of ways to reciprocally link elements of an n X 4 array either to themselves or to exactly one king-move neighbor.
%C A220640 Column 4 of A220644.
%H A220640 Alois P. Heinz, <a href="/A220640/b220640.txt">Table of n, a(n) for n = 0..300</a> (terms n = 1..210 from R. H. Hardin)
%F A220640 Empirical: a(n) = 20*a(n-1) +114*a(n-2) -325*a(n-3) -340*a(n-4) +460*a(n-5) +245*a(n-6) -48*a(n-7) +2*a(n-8) -15*a(n-9).
%F A220640 G.f.: -(3*x^7 -x^6 +14*x^5 -58*x^4 -70*x^3 +42*x^2 +15*x-1) / (15*x^9 -2*x^8 +48*x^7 -245*x^6 -460*x^5 +340*x^4 +325*x^3 -114*x^2 -20*x+1). - _Alois P. Heinz_, Jun 03 2014
%e A220640 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 A220640 ..9..9..0..0....0..0..0..8....8..6..4..0....6..4..8..0....8..0..0..7
%e A220640 ..8..1..1..0....9..7..0..2....2..0..8..8....0..0..2..0....2..8..3..0
%e A220640 ..2..6..4..0....3..1..6..4....6..4..2..2....6..4..6..4....0..2..0..0
%p A220640 gf:= -(3*x^7 -x^6 +14*x^5 -58*x^4 -70*x^3 +42*x^2 +15*x-1) / (15*x^9 -2*x^8 +48*x^7 -245*x^6 -460*x^5 +340*x^4 +325*x^3 -114*x^2 -20*x+1):
%p A220640 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A220640 seq(a(n), n=0..30);  # _Alois P. Heinz_, Jun 03 2014
%K A220640 nonn
%O A220640 0,2
%A A220640 _R. H. Hardin_, Dec 17 2012