A267474 Number of length-6 0..n arrays with no following elements larger than the first repeated value.

38, 418, 2490, 10119, 31880, 83972, 193852, 404589, 779938, 1410134, 2418406, 3968211, 6271188, 9595832, 14276888, 20725465, 29439870, 41017162, 56165426, 75716767, 100641024, 132060204, 171263636, 219723845, 279113146, 351320958

Offset

1,1

Comments

Row 6 of A267471.

Links

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

Formula

Empirical: a(n) = n^6 + (197/60)*n^5 + 7*n^4 + (43/4)*n^3 + 10*n^2 + (149/30)*n + 1.

Conjectures from Colin Barker, Feb 05 2018: (Start)

G.f.: x*(38 + 152*x + 362*x^2 + 137*x^3 + 37*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=7:
..0....6....6....4....1....2....0....0....2....0....2....4....0....2....6....4
..5....3....3....2....4....1....7....1....0....6....1....5....2....0....5....6
..1....2....5....5....0....6....2....7....2....7....6....3....6....1....7....2
..6....6....6....2....2....5....3....3....6....7....7....0....2....0....0....0
..1....2....1....6....6....7....7....1....6....3....7....4....3....5....3....7
..5....5....0....1....6....4....2....6....6....1....1....7....1....0....1....4

Crossrefs

Cf. A267471.

Sequence in context: A159943 A221634 A251056 * A240258 A254471 A039685

Adjacent sequences: A267471 A267472 A267473 * A267475 A267476 A267477

Keyword

nonn

Author

R. H. Hardin, Jan 15 2016

Status

approved