A247728 Number of length 2+3 0..n arrays with no disjoint pairs in any consecutive four terms having the same sum

8, 90, 456, 1592, 4344, 10098, 20816, 39264, 69000, 114650, 181848, 277560, 409976, 588882, 825504, 1132928, 1525896, 2021274, 2637800, 3396600, 4320888, 5436530, 6771696, 8357472, 10227464, 12418458, 14969976, 17924984, 21329400, 25232850

Offset

1,1

Comments

Row 2 of A247726

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -4*a(n-2) -4*a(n-3) +10*a(n-4) -4*a(n-5) -4*a(n-6) +4*a(n-7) -a(n-8)

Empirical for n mod 2 = 0: a(n) = 1*n^5 + 1*n^4 + (9/2)*n^3 + (3/2)*n^2

Empirical for n mod 2 = 1: a(n) = 1*n^5 + 1*n^4 + (9/2)*n^3 + (3/2)*n^2 - (3/2)*n + (3/2).

Empirical G.f.: 2*x*(4+29*x+64*x^2+80*x^3+40*x^4+23*x^5) / ( (1+x)^2*(x-1)^6 ). - R. J. Mathar, Sep 23 2014

Example

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

Crossrefs

Sequence in context: A371208 A077192 A128304 * A056784 A166769 A323960

Adjacent sequences: A247725 A247726 A247727 * A247729 A247730 A247731

Keyword

nonn

Author

R. H. Hardin, Sep 23 2014

Status

approved