A211562 Number of nonnegative integer arrays of length n+2 with new values 0 upwards introduced in order, and containing the value n-1.

5, 14, 36, 81, 162, 295, 499, 796, 1211, 1772, 2510, 3459, 4656, 6141, 7957, 10150, 12769, 15866, 19496, 23717, 28590, 34179, 40551, 47776, 55927, 65080, 75314, 86711, 99356, 113337, 128745, 145674, 164221, 184486, 206572, 230585, 256634, 284831

Offset

1,1

Comments

Row 3 of A211561.

Links

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

Formula

Empirical: a(n) = (1/8)*n^4 + (5/12)*n^3 + (7/8)*n^2 + (19/12)*n + 2.

Empirical: a(n) = sum{j in n..n+2}stirling2(n+2,j).

Conjectures from Colin Barker, Jul 19 2018: (Start)

G.f.: x*(5 - 11*x + 16*x^2 - 9*x^3 + 2*x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

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

Crossrefs

Cf. A211561.

Sequence in context: A142585 A332743 A234097 * A261055 A320853 A193557

Adjacent sequences: A211559 A211560 A211561 * A211563 A211564 A211565

Keyword

nonn

Author

R. H. Hardin, Apr 15 2012

Status

approved