A200273 Number of 0..n arrays x(0..5) of 6 elements with zero 3rd differences.

2, 3, 6, 9, 14, 25, 36, 47, 64, 87, 110, 143, 176, 209, 258, 311, 364, 431, 498, 575, 666, 761, 856, 969, 1092, 1219, 1364, 1513, 1662, 1847, 2032, 2221, 2432, 2647, 2876, 3135, 3394, 3657, 3946, 4257, 4568, 4913, 5258, 5607, 6004, 6409, 6814, 7257, 7700, 8169

Offset

1,1

Comments

Row 4 of A200272.

Links

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

Formula

Empirical: a(n) = a(n-3) +a(n-5) +a(n-6) -a(n-8) -a(n-9) +a(n-10) -a(n-11) -a(n-13) +a(n-14) -a(n-15) -a(n-16) +a(n-18) +a(n-19) +a(n-21) -a(n-24).

Empirical g.f.: x*(2 + 3*x + 6*x^2 + 7*x^3 + 11*x^4 + 17*x^5 + 22*x^6 + 24*x^7 + 26*x^8 + 33*x^9 + 31*x^10 + 32*x^11 + 26*x^12 + 26*x^13 + 21*x^14 + 15*x^15 + 10*x^16 + 8*x^17 + 6*x^18 + 3*x^19 + 3*x^20 + x^21 - x^23) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x + x^2)^2*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)^2). - Colin Barker, May 20 2018

Example

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

Crossrefs

Cf. A200272.

Sequence in context: A147007 A146937 A032231 * A303664 A190276 A113808

Adjacent sequences: A200270 A200271 A200272 * A200274 A200275 A200276

Keyword

nonn

Author

R. H. Hardin, Nov 15 2011

Status

approved