A241938 Number of length 2+4 0..n arrays with no consecutive five elements summing to more than 2*n.

26, 218, 1043, 3599, 10031, 24052, 51570, 101421, 186208, 323246, 535613, 853307, 1314509, 1966952, 2869396, 4093209, 5724054, 7863682, 10631831, 14168231, 18634715, 24217436, 31129190, 39611845, 49938876, 62418006, 77393953, 95251283

Offset

1,1

Links

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

Formula

Empirical: a(n) = (53/360)*n^6 + (5/4)*n^5 + (307/72)*n^4 + (91/12)*n^3 + (683/90)*n^2 + (25/6)*n + 1.

Conjectures from Colin Barker, Oct 30 2018: (Start)

G.f.: x*(26 + 36*x + 63*x^2 - 34*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Row 2 of A241936.

Sequence in context: A125363 A126521 A242262 * A317865 A185553 A269658

Adjacent sequences: A241935 A241936 A241937 * A241939 A241940 A241941

Keyword

nonn

Author

R. H. Hardin, May 02 2014

Status

approved