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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 R. H. Hardin, Table of n, a(n) for n = 1..210 Robert Israel, Maple-assisted proof of formula 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 Adjacent sequences: A221566 A221567 A221568 * A221570 A221571 A221572 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.)