A204216 Number of length 8 nonnegative integer arrays starting and ending with 0 with adjacent elements differing by no more than n.

127, 1925, 12492, 51945, 164255, 431445, 991152, 2057553, 3945655, 7098949, 12120428, 19806969, 31187079, 47562005, 70550208, 102135201, 144716751, 201165445, 274880620, 369851657, 490722639, 642860373, 832425776, 1066448625

Offset

1,1

Comments

Row 7 of A204213.

Links

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

Formula

Empirical: a(n) = (841/180)*n^6 + (101/5)*n^5 + (1325/36)*n^4 + (73/2)*n^3 + (946/45)*n^2 + (34/5)*n + 1.

Conjectures from Colin Barker, Jun 06 2018: (Start)

G.f.: x*(127 + 1036*x + 1684*x^2 + 481*x^3 + 42*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:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..2....3....3....2....3....2....3....4....1....4....4....4....1....4....3....3
..3....5....0....2....2....0....6....0....1....4....8....8....1....6....5....2
..4....4....1....5....5....2....8....2....1....5....5....4....0....9....7....3
..4....5....3....7....6....3....6....6....4....2....3....2....1....6...10....1
..7....4....6....7....6....2....2....3....3....0....6....1....3....2....6....2
..4....2....4....4....3....0....2....4....2....1....4....0....4....1....3....1
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Cf. A204213.

Sequence in context: A025598 A115153 A172408 * A075937 A075938 A258003

Adjacent sequences: A204213 A204214 A204215 * A204217 A204218 A204219

Keyword

nonn

Author

R. H. Hardin, Jan 12 2012

Status

approved