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

Author

R. H. Hardin, Jan 12 2012

Keywords

• nonn

Comments

Row 7 of A204213.

Examples

			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
		

Links

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

Crossrefs

Cf. A204213.

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)