A253130 Number of length 2+2 0..n arrays with the sum of medians of adjacent triples multiplied by some arrangement of +-1 equal to zero.

12, 53, 152, 345, 676, 1197, 1968, 3057, 4540, 6501, 9032, 12233, 16212, 21085, 26976, 34017, 42348, 52117, 63480, 76601, 91652, 108813, 128272, 150225, 174876, 202437, 233128, 267177, 304820, 346301, 391872, 441793, 496332, 555765, 620376, 690457

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/3)*n^4 + (8/3)*n^3 + (14/3)*n^2 + (10/3)*n + 1.

Conjectures from Colin Barker, Dec 09 2018: (Start)

G.f.: x*(3 - x)*(4 - x + 2*x^2 - x^3) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

Some solutions for n=10:
..7....4....7....9....1....4....7....6....5....4....4....4....6....9....9....1
..2....6...10....0....2....1...10....7....9....6...10....0....6....2....5....6
..0....9....9....1....9....0....9...10....8....8....6....3....7....1....9....3
..4....0....4....3....2....1....5....3....1....6....6....7....2....4....9....2

Crossrefs

Row 2 of A253129.

Sequence in context: A307916 A280660 A268186 * A213549 A211060 A242514

Adjacent sequences: A253127 A253128 A253129 * A253131 A253132 A253133

Keyword

nonn

Author

R. H. Hardin, Dec 27 2014

Status

approved