A200555 Number of -n..n arrays x(0..4) of 5 elements with zero sum and nonzero second differences.

26, 280, 1184, 3396, 7778, 15476, 27806, 46346, 72902, 109528, 158422, 222162, 303412, 405134, 530518, 683014, 866156, 1083954, 1340420, 1639900, 1986968, 2386470, 2843276, 3362828, 3950486, 4611980, 5353268, 6180592, 7100158, 8118840

Offset

1,1

Comments

Row 3 of A200553.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = a(n-1) +2*a(n-2) -3*a(n-4) -3*a(n-5) +3*a(n-6) +3*a(n-7) -2*a(n-9) -a(n-10) +a(n-11).

Empirical g.f.: 2*x*(13 + 127*x + 426*x^2 + 826*x^3 + 1046*x^4 + 912*x^5 + 544*x^6 + 205*x^7 + 37*x^8 + 4*x^9) / ((1 - x)^5*(1 + x)^2*(1 + x + x^2)^2). - Colin Barker, May 21 2018

Example

Some solutions for n=3:
..3...-2...-3....0...-2....3...-2....2...-3...-2...-1....2....1....2...-2....3
..0...-3....2...-1....3...-1...-2....2....3....3....1....2....1...-2....1...-1
.-2....1....1....3....0....1....2...-1....0...-3...-2...-2...-2....2...-3...-3
..2....2....1...-2....1...-3....1...-2....2...-1....2....1...-1...-3....1....2
.-3....2...-1....0...-2....0....1...-1...-2....3....0...-3....1....1....3...-1

Crossrefs

Cf. A200553.

Sequence in context: A186261 A006045 A022686 * A130901 A336732 A227332

Adjacent sequences: A200552 A200553 A200554 * A200556 A200557 A200558

Keyword

nonn

Author

R. H. Hardin, Nov 19 2011

Status

approved