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

1, 8, 728, 37320, 2226936, 128171936, 7444342896, 431408410784, 25014514225856, 1450226501771584, 84080327982982848, 4874715696405194752, 282621433306639435392, 16385536749696632356608, 949984033027704106955264, 55077209132605857634211328

Offset

0,2

Comments

Column 5 of A220644.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300 (terms n = 1..210 from R. H. Hardin)

Formula

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).

G.f.: see Maple program. - Alois P. Heinz, Jun 03 2014

Example

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)
..0..6..4..9..0....6..4..0..0..7....0..9..0..6..4....0..7..6..4..0
..6..4..0..8..1....0..7..7..3..0....0..7..1..0..0....3..9..0..9..0
..0..0..0..2..0....3..3..0..0..0....3..0..0..6..4....0..0..1..0..1

Maple

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):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..25);  # Alois P. Heinz, Jun 03 2014

Crossrefs

Sequence in context: A071308 A046188 A014387 * A017007 A268250 A268106

Adjacent sequences: A220638 A220639 A220640 * A220642 A220643 A220644

Keyword

nonn

Author

R. H. Hardin, Dec 17 2012

Status

approved