A202753 Number of n X 5 nonnegative integer arrays with each row and column increasing from zero by 0 or 1.

1, 5, 31, 184, 924, 3809, 13197, 39675, 106357, 259669, 586829, 1242946, 2491516, 4763097, 8738111, 15461061, 26494977, 44126629, 71634979, 113637500, 176531380, 269049265, 402952089, 593884703, 862423461, 1235348661, 1747178785

Offset

1,2

Comments

Column 5 of A202756.

Links

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

Formula

Empirical: a(n) = (1/302400)*n^10 + (1/10080)*n^9 + (1/1008)*n^8 + (1/336)*n^7 - (67/14400)*n^6 + (7/480)*n^5 + (1021/6048)*n^4 - (145/1008)*n^3 + (10519/12600)*n^2 - (367/420)*n + 1.

Conjectures from Colin Barker, Jun 01 2018: (Start)

G.f.: x*(1 - 6*x + 31*x^2 - 47*x^3 + 110*x^4 - 162*x^5 + 140*x^6 - 79*x^7 + 31*x^8 - 8*x^9 + x^10) / (1 - x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.

(End)

Example

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

Crossrefs

Cf. A202756.

Sequence in context: A180635 A078526 A255236 * A057426 A329014 A015540

Adjacent sequences: A202750 A202751 A202752 * A202754 A202755 A202756

Keyword

nonn

Author

R. H. Hardin, Dec 23 2011

Status

approved