A253132 Number of length 4+2 0..n arrays with the sum of medians of adjacent triples multiplied by some arrangement of +-1 equal to zero

40, 393, 2058, 7257, 19990, 46945, 98124, 187593, 335106, 566597, 915078, 1423385, 2144128, 3140689, 4491642, 6289609, 8642310, 11679353, 15549300, 20420721, 26492194, 33986741, 43152838, 54278609, 67682648, 83714937, 102776362

Offset

1,1

Comments

Row 4 of A253129

Links

R. H. Hardin, Table of n, a(n) for n = 1..64

Formula

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +5*a(n-3) -12*a(n-4) +12*a(n-5) -10*a(n-6) +18*a(n-7) -18*a(n-8) +10*a(n-9) -12*a(n-10) +12*a(n-11) -5*a(n-12) +3*a(n-13) -3*a(n-14) +a(n-15)

Empirical for n mod 3 = 0: a(n) = (2/15)*n^6 + (1273/405)*n^5 + (298/27)*n^4 + (601/81)*n^3 + (143/15)*n^2 + (238/45)*n + 1

Empirical for n mod 3 = 1: a(n) = (2/15)*n^6 + (1273/405)*n^5 + (298/27)*n^4 + (203/27)*n^3 + (4001/405)*n^2 + (32/5)*n + (17/9)

Empirical for n mod 3 = 2: a(n) = (2/15)*n^6 + (1273/405)*n^5 + (298/27)*n^4 + (601/81)*n^3 + (3781/405)*n^2 + (218/45)*n + (73/81)

Example

Some solutions for n=8
..8....0....8....3....6....1....3....8....3....1....2....0....1....7....3....6
..2....2....1....5....2....1....3....0....1....2....3....1....4....3....3....2
..4....8....3....4....3....7....2....0....0....0....3....6....2....1....0....3
..2....0....1....5....8....1....4....6....3....0....5....7....6....7....5....7
..6....2....0....8....8....4....5....5....8....1....7....1....2....1....6....5
..6....7....8....6....1....4....2....0....3....8....2....0....4....8....4....3

Crossrefs

Sequence in context: A229716 A221820 A301528 * A293969 A168192 A251129

Adjacent sequences: A253129 A253130 A253131 * A253133 A253134 A253135

Keyword

nonn

Author

R. H. Hardin, Dec 27 2014

Status

approved