A241939 Number of length 3+4 0..n arrays with no consecutive five elements summing to more than 2*n.

43, 509, 3150, 13339, 44063, 122162, 297324, 654345, 1329163, 2529175, 4558346, 7847619, 12991135, 20788772, 32295512, 48878145, 72279819, 104692945, 148840966, 208069499, 286447359, 388877974, 521221700, 690429545, 904688811

Offset

1,1

Links

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

Formula

Empirical: a(n) = (509/5040)*n^7 + 1*n^6 + (743/180)*n^5 + (223/24)*n^4 + (8993/720)*n^3 + (245/24)*n^2 + (502/105)*n + 1.

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

G.f.: x*(43 + 165*x + 282*x^2 - 17*x^3 + 57*x^4 - 28*x^5 + 8*x^6 - x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

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

Crossrefs

Row 3 of A241936.

Sequence in context: A184145 A238202 A008388 * A251896 A060888 A245427

Adjacent sequences: A241936 A241937 A241938 * A241940 A241941 A241942

Keyword

nonn

Author

R. H. Hardin, May 02 2014

Status

approved