A211687 - OEIS

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A211687

Number of -4..4 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having three distinct values for every i<=n and j<=n.

68, 156, 318, 604, 1144, 2108, 3924, 7236, 13486, 25108, 47168, 88856, 168588, 321220, 615390, 1184204, 2288040, 4438780, 8636484, 16862164, 32990542, 64729172, 127184496, 250474872, 493763644, 975154132, 1927138430, 3814135532

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 4*a(n-1) + 6*a(n-2) - 41*a(n-3) + 6*a(n-4) + 154*a(n-5) - 109*a(n-6) - 256*a(n-7) + 262*a(n-8) + 175*a(n-9) - 230*a(n-10) - 30*a(n-11) + 60*a(n-12).

Empirical g.f.: 2*x*(34 - 58*x - 357*x^2 + 592*x^3 + 1404*x^4 - 2231*x^5 - 2564*x^6 + 3806*x^7 + 2164*x^8 - 2860*x^9 - 668*x^10 + 704*x^11) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)*(1 - 5*x^2 + 5*x^4)). - Colin Barker, Jul 19 2018

EXAMPLE

Some solutions for n=5:

..2....1....0....0...-2....3...-4...-2...-2...-3...-1....1....0...-1....0....3

..0....2....2...-4....3....4....4....0...-1...-1....2....3...-2....1....4...-3

..2....1....0....2....1....3...-4....1....0....1....0....1....0....0...-4....0

..0....2...-2...-4....3....2....4....2....2...-1...-4...-2....2....1....0....3

.-4...-4....2....0...-2....3...-4....1....0....1....0....1...-2...-1....4....0

..4....2....0...-4....3....2....0....0...-1....3....2....3....2....0....0....3

CROSSREFS

Sequence in context: A044700 A063341 A118214 * A256023 A044400 A044781

Adjacent sequences: A211684 A211685 A211686 * A211688 A211689 A211690

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 18 2012

STATUS

approved