login
A299137
Number of n X 3 0..1 arrays with every element equal to 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.
1
1, 18, 129, 899, 6205, 43066, 298361, 2068149, 14334327, 99354814, 688646455, 4773147461, 33083623049, 229309139316, 1589386941041, 11016355018433, 76356533603993, 529242224053012, 3668282443014641, 25425590535640541
OFFSET
1,2
COMMENTS
Column 3 of A299142.
LINKS
FORMULA
Empirical: a(n) = 6*a(n-1) +8*a(n-2) -12*a(n-3) +8*a(n-4) +7*a(n-5) -4*a(n-6) -2*a(n-7) -7*a(n-8) -5*a(n-9) +2*a(n-10) for n>11.
Empirical g.f.: x*(1 + 12*x + 13*x^2 - 7*x^3 - 13*x^4 + 41*x^5 - 41*x^6 - 106*x^7 - 37*x^8 + 14*x^9 + 2*x^10) / ((1 - x)*(1 - 5*x - 13*x^2 - x^3 - 9*x^4 - 16*x^5 - 12*x^6 - 10*x^7 - 3*x^8 + 2*x^9)). - Colin Barker, Feb 17 2018
EXAMPLE
Some solutions for n=5:
..0..0..1. .0..0..0. .0..1..1. .0..1..1. .0..0..1. .0..1..1. .0..0..1
..1..0..1. .0..1..0. .0..1..0. .0..0..1. .1..1..0. .1..0..0. .0..0..1
..1..1..0. .0..0..1. .0..1..0. .1..0..0. .0..0..1. .0..1..1. .1..0..1
..1..0..0. .1..1..0. .0..0..0. .1..0..1. .0..1..0. .0..0..1. .0..1..0
..0..1..1. .1..0..1. .0..0..0. .1..1..0. .1..0..1. .1..1..1. .1..0..0
CROSSREFS
Cf. A299142.
Sequence in context: A244879 A142965 A298275 * A299368 A299932 A058649
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 03 2018
STATUS
approved