login
A202901
Number of n X 3 0..1 arrays with every one equal to some NW, E or S neighbor.
1
1, 14, 93, 494, 2801, 16062, 91161, 517646, 2942681, 16724094, 95039817, 540117614, 3069530009, 17444277726, 99136698537, 563399082830, 3201826086713, 18196142535870, 103409617841865, 587682198231086, 3339828270813785
OFFSET
1,2
FORMULA
Empirical: a(n) = 8*a(n-1) -17*a(n-2) +32*a(n-3) -70*a(n-4) +72*a(n-5) -24*a(n-6).
Formula verified by Robert Israel, May 09 2018 (see link).
G.f.: x*(1 + 6*x - 2*x^2 - 44*x^3 + 52*x^4 - 16*x^5) / ((1 - x)*(1 - 7*x + 10*x^2 - 22*x^3 + 48*x^4 - 24*x^5)). - Colin Barker, Jun 02 2018
EXAMPLE
Some solutions for n=5:
0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0
1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 0
1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1
1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1
0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0
MAPLE
f:= gfun:-rectoproc({a(n) = 8*a(n-1) -17*a(n-2) +32*a(n-3) -70*a(n-4) +72*a(n-5) -24*a(n-6), seq(a(i)=[1, 14, 93, 494, 2801, 16062][i], i=1..6)},
a(n), remember):
map(f, [$1..25]); # Robert Israel, May 09 2018
MATHEMATICA
LinearRecurrence[{8, -17, 32, -70, 72, -24}, {1, 14, 93, 494, 2801, 16062}, 21] (* Jean-François Alcover, Aug 26 2022 *)
CROSSREFS
Column 3 of A202906.
Sequence in context: A022609 A060217 A113776 * A224328 A241396 A370721
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Dec 25 2011
STATUS
approved