A224392 Number of 3 X n 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

64, 1000, 6094, 27790, 102232, 319769, 881519, 2196522, 5038720, 10788462, 21789398, 41858498, 76994510, 136338455, 233448747, 387963222, 627730762, 991506308, 1532314870, 2321602662, 3454306716, 5054988261, 7285189791

Offset

1,1

Comments

Row 3 of A224391.

Links

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

Formula

Empirical: a(n) = (353/181440)*n^9 + (17/560)*n^8 + (9731/30240)*n^7 + (1283/720)*n^6 + (52457/8640)*n^5 + (776/45)*n^4 + (294499/11340)*n^3 + (28837/2520)*n^2 + (8207/126)*n - 18 for n>1.

Conjectures from Colin Barker, Aug 30 2018: (Start)

G.f.: x*(64 + 360*x - 1026*x^2 + 4170*x^3 - 7998*x^4 + 10591*x^5 - 9351*x^6 + 5629*x^7 - 2165*x^8 + 478*x^9 - 46*x^10) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>11.

(End)

Example

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

Crossrefs

Cf. A224391.

Sequence in context: A224162 A224413 A016959 * A224025 A270272 A297612

Adjacent sequences: A224389 A224390 A224391 * A224393 A224394 A224395

Keyword

nonn

Author

R. H. Hardin, Apr 05 2013

Status

approved