A250880 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A250880

Number of (3+1) X (n+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.

2002, 6812, 16262, 31928, 55386, 88212, 131982, 188272, 258658, 344716, 448022, 570152, 712682, 877188, 1065246, 1278432, 1518322, 1786492, 2084518, 2413976, 2776442, 3173492, 3606702, 4077648, 4587906, 5139052, 5732662, 6370312, 7053578

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = (788/3)*n^3 + 744*n^2 + (2218/3)*n + 256.

Conjectures from Colin Barker, Nov 22 2018: (Start)

G.f.: 2*x*(1001 - 598*x + 513*x^2 - 128*x^3) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)

EXAMPLE

Some solutions for n=4:

..2..3..3..3..3....3..3..3..2..2....3..3..3..3..3....0..0..0..0..0

..1..2..2..2..2....2..2..2..3..3....2..2..2..2..2....2..2..2..3..3

..0..2..2..2..2....1..1..1..3..3....1..1..1..1..2....1..1..1..3..3

..0..3..3..3..3....0..0..0..2..3....0..2..2..2..3....0..0..0..2..2

CROSSREFS

Row 3 of A250877.

Sequence in context: A162238 A162239 A104400 * A154049 A339803 A108116

Adjacent sequences: A250877 A250878 A250879 * A250881 A250882 A250883

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 28 2014

STATUS

approved