A211564 Number of nonnegative integer arrays of length n+4 with new values 0 upwards introduced in order, and containing the value n-1.

52, 202, 813, 3046, 10096, 29503, 77078, 183074, 401337, 822277, 1590604, 2928879, 5168035, 8786128, 14456683, 23108105, 35995730, 54788196, 81669919, 119461564, 171760506, 243103381, 339152932, 466911460, 634963295, 853748807, 1135872582

Offset

1,1

Comments

Row 5 of A211561.

Links

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

Formula

Empirical: a(n) = (1/384)*n^8 + (1/32)*n^7 + (95/576)*n^6 + (71/120)*n^5 + (2155/1152)*n^4 + (167/32)*n^3 + (3301/288)*n^2 + (2119/120)*n + 15.

Empirical: a(n) = sum{j in n..n+4}stirling2(n+4,j).

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

G.f.: x*(52 - 266*x + 867*x^2 - 1367*x^3 + 1534*x^4 - 1097*x^5 + 497*x^6 - 130*x^7 + 15*x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(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....0....1....1....1....1....1....0....1....1....1....1
..2....1....2....2....2....1....2....2....2....2....2....1....0....2....0....2
..3....0....3....1....0....2....3....3....2....0....2....0....1....3....2....3
..4....2....2....0....3....0....4....4....3....1....1....2....2....3....2....0
..5....3....2....3....4....3....2....4....3....3....3....3....2....2....2....4
..5....2....1....3....1....4....5....1....4....3....1....3....3....4....3....1
..4....0....4....4....0....3....0....1....5....4....4....2....0....5....0....0
..1....4....5....4....2....4....0....1....3....0....0....4....4....6....4....1

Crossrefs

Cf. A211561.

Sequence in context: A161478 A288919 A260549 * A346825 A346858 A251287

Adjacent sequences: A211561 A211562 A211563 * A211565 A211566 A211567

Keyword

nonn

Author

R. H. Hardin, Apr 15 2012

Status

approved