|
| |
|
|
A205345
|
|
Number of length 8 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than n.
|
|
1
|
|
|
|
0, 272, 3272, 18652, 71630, 214724, 542850, 1211784, 2459988, 4633800, 8215988, 13857668, 22413586, 34980764, 52940510, 78003792, 112259976, 158228928, 218916480, 297873260, 399256886, 527897524, 689366810, 890050136, 1137222300
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Row 7 of A205341.
|
|
|
LINKS
|
R. H. Hardin, Table of n, a(n) for n = 1..210
|
|
|
FORMULA
|
Empirical: a(n) = (841/180)*n^6 - (1/3)*n^5 - (19/36)*n^4 + (1/3)*n^3 - (103/90)*n^2 - 3*n.
Conjectures from Colin Barker, Jun 11 2018: (Start)
G.f.: 2*x^2*(136 + 684*x + 730*x^2 + 129*x^3 + 3*x^4) / (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=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..5....3....5....2....2....2....2....3....5....3....1....2....4....2....3....4
..6....7....8....6....3....4....4....4....9....5....2....5....8....6....5....7
..7....8...11....7....4....3....2....7...12....1....0....4....7....4....6....8
.10....4....9....6....3....6....7....3....7....2....4....3....3....8....3....7
..6....5....4....4....0....5....3....6....3....7....6....0....1....3....1....8
..5....3....2....3....3....4....4....2....5....2....5....2....5....5....3....3
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
|
|
|
CROSSREFS
|
Cf. A205341.
Sequence in context: A305952 A317213 A178268 * A302899 A266106 A264077
Adjacent sequences: A205342 A205343 A205344 * A205346 A205347 A205348
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
R. H. Hardin, Jan 26 2012
|
|
|
STATUS
|
approved
|
| |
|
|
