A200083 Number of 0..n arrays x(0..4) of 5 elements with zero 3rd differences.

2, 3, 8, 17, 26, 43, 64, 89, 122, 163, 208, 269, 334, 407, 496, 597, 702, 831, 968, 1117, 1286, 1471, 1664, 1889, 2122, 2371, 2648, 2945, 3250, 3595, 3952, 4329, 4738, 5171, 5616, 6109, 6614, 7143, 7712, 8309, 8918, 9583, 10264, 10973, 11726, 12511, 13312

Offset

1,1

Comments

Row 4 of A200082.

Links

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

Formula

Empirical: a(n) = a(n-1) +a(n-3) -a(n-5) +a(n-6) -2*a(n-7) +a(n-8) -a(n-9) +a(n-11) +a(n-13) -a(n-14).

Empirical g.f.: x*(2 + x + 5*x^2 + 7*x^3 + 6*x^4 + 11*x^5 + 5*x^6 + 8*x^7 + 3*x^8 + x^9 + 2*x^10 + x^11 + x^12 - x^13) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, May 17 2018

Example

Some solutions for n=6:
..2....1....2....3....0....4....0....5....0....6....6....3....6....0....4....3
..3....3....4....4....4....4....0....6....3....2....3....3....3....1....3....5
..3....4....5....4....6....4....0....6....4....0....2....3....1....2....2....6
..2....4....5....3....6....4....0....5....3....0....3....3....0....3....1....6
..0....3....4....1....4....4....0....3....0....2....6....3....0....4....0....5

Crossrefs

Cf. A200082.

Sequence in context: A005648 A113947 A102008 * A210701 A158921 A064954

Adjacent sequences: A200080 A200081 A200082 * A200084 A200085 A200086

Keyword

nonn

Author

R. H. Hardin, Nov 13 2011

Status

approved