A250628 Number of (n+1)X(4+1) 0..2 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction

2183, 12360, 56232, 218680, 747039, 2290189, 6421141, 16675794, 40596068, 93379730, 204479885, 428521374, 863721166, 1680656753, 3168130907, 5801678648, 10347803205, 18014202504, 30669676297, 51151865140, 83703408057

Offset

1,1

Comments

Column 4 of A250632

Links

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

Formula

Empirical: a(n) = 9*a(n-1) -30*a(n-2) +30*a(n-3) +75*a(n-4) -243*a(n-5) +152*a(n-6) +360*a(n-7) -690*a(n-8) +130*a(n-9) +780*a(n-10) -780*a(n-11) -130*a(n-12) +690*a(n-13) -360*a(n-14) -152*a(n-15) +243*a(n-16) -75*a(n-17) -30*a(n-18) +30*a(n-19) -9*a(n-20) +a(n-21) for n>24

Empirical for n mod 2 = 0: a(n) = (1/7264857600)*n^14 + (1/46126080)*n^13 + (509/319334400)*n^12 + (9587/159667200)*n^11 + (3083/2419200)*n^10 + (4243/241920)*n^9 + (81563423/406425600)*n^8 + (8764057/4838400)*n^7 + (9317323/907200)*n^6 + (34764997/725760)*n^5 + (2064044711/13305600)*n^4 + (113560957/277200)*n^3 + (871250902/1576575)*n^2 + (56045677/60060)*n + 12

Empirical for n mod 2 = 1: a(n) = (1/7264857600)*n^14 + (1/46126080)*n^13 + (509/319334400)*n^12 + (9587/159667200)*n^11 + (3083/2419200)*n^10 + (4243/241920)*n^9 + (81563423/406425600)*n^8 + (8764057/4838400)*n^7 + (9317323/907200)*n^6 + (34777093/725760)*n^5 + (2080122311/13305600)*n^4 + (905732981/2217600)*n^3 + (420887318849/807206400)*n^2 + (15772405601/15375360)*n - (250753/4096)

Example

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

Crossrefs

Sequence in context: A254417 A254424 A343777 * A234733 A371474 A067263

Adjacent sequences: A250625 A250626 A250627 * A250629 A250630 A250631

Keyword

nonn

Author

R. H. Hardin, Nov 26 2014

Status

approved