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A221569 Number of 0..4 arrays of length n with each element differing from at least one neighbor by something other than 1. 1
0, 17, 59, 289, 1293, 5913, 26911, 122621, 558547, 2544357, 11590169, 52796369, 240501763, 1095550873, 4990531051, 22733220441, 103555975477, 471725515497, 2148837489879, 9788536778149, 44589436230083, 203116958964733 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Empirical: a(n) = 5*a(n-1) -3*a(n-2) +a(n-3) +15*a(n-4) +3*a(n-5) for n>6.
Empirical g.f.: -x^2*(17-26*x+45*x^2+8*x^3+x^4) / ( -1+5*x-3*x^2+x^3+15*x^4+3*x^5 ). - R. J. Mathar, Jun 06 2013
Formula verified by Robert Israel, Jun 04 2018: see link.
EXAMPLE
Some solutions for n=6
..4....2....2....2....3....4....2....2....4....0....3....2....0....4....4....4
..4....2....4....4....0....4....0....0....0....0....3....4....0....4....1....2
..2....1....0....1....0....4....2....1....3....0....0....3....3....2....0....2
..0....4....3....1....4....1....4....4....1....0....0....0....3....2....0....2
..3....3....0....1....0....2....0....2....0....4....3....2....4....4....3....1
..1....3....3....3....3....2....0....0....4....0....0....4....0....4....3....3
MAPLE
f:= gfun:-rectoproc({a(n) = 5*a(n-1) -3*a(n-2) +a(n-3) +15*a(n-4) +3*a(n-5), seq(a(i)=[0, 17, 59, 289, 1293, 5913][i], i=1..6)},
a(n), remember):
map(f, [$1..50]); # Robert Israel, Jun 04 2018
CROSSREFS
Column 4 of A221573.
Sequence in context: A176783 A086816 A243096 * A179816 A094207 A156912
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 20 2013
STATUS
approved

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Last modified June 21 09:15 EDT 2024. Contains 373542 sequences. (Running on oeis4.)