A250630 Number of (n+1)X(6+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

28456, 190213, 994030, 4416061, 17202711, 60472234, 195029867, 584383121, 1641320797, 4350649060, 10946535213, 26264135834, 60344532228, 133238716551, 283638236272, 583811316064, 1164928298365, 2258673657000, 4264498245386

Offset

1,1

Comments

Column 6 of A250632

Links

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

Formula

Empirical: a(n) = 9*a(n-1) -28*a(n-2) +12*a(n-3) +134*a(n-4) -294*a(n-5) -28*a(n-6) +876*a(n-7) -919*a(n-8) -833*a(n-9) +2312*a(n-10) -680*a(n-11) -2380*a(n-12) +2380*a(n-13) +680*a(n-14) -2312*a(n-15) +833*a(n-16) +919*a(n-17) -876*a(n-18) +28*a(n-19) +294*a(n-20) -134*a(n-21) -12*a(n-22) +28*a(n-23) -9*a(n-24) +a(n-25) for n>36

Empirical for n mod 2 = 0: a(n) = (677/10461394944000)*n^16 + (323/32691859200)*n^15 + (328303/523069747200)*n^14 + (23351/1067489280)*n^13 + (26884057/57480192000)*n^12 + (19162687/2874009600)*n^11 + (264304657/3657830400)*n^10 + (282962783/365783040)*n^9 + (546703353947/73156608000)*n^8 + (9006721609/261273600)*n^7 + (606619175047/2874009600)*n^6 + (5364465529/35925120)*n^5 + (1489177450559837/72648576000)*n^4 - (52712541330373/363242880)*n^3 + (55868420400113/100900800)*n^2 - (20512474811/60060)*n - 1864584 for n>11

Empirical for n mod 2 = 1: a(n) = (677/10461394944000)*n^16 + (323/32691859200)*n^15 + (328303/523069747200)*n^14 + (23351/1067489280)*n^13 + (26884057/57480192000)*n^12 + (19162687/2874009600)*n^11 + (264304657/3657830400)*n^10 + (282962783/365783040)*n^9 + (546703353947/73156608000)*n^8 + (9007343689/261273600)*n^7 + (607505328007/2874009600)*n^6 + (10667540267/71850240)*n^5 + (1489289213961587/72648576000)*n^4 - (422056644097481/2905943040)*n^3 + (1787002967118631/3228825600)*n^2 - (863144758907/2562560)*n - (3842277903/2048)for n>11

Example

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

Crossrefs

Sequence in context: A202614 A270855 A250992 * A236595 A083611 A083612

Adjacent sequences: A250627 A250628 A250629 * A250631 A250632 A250633

Keyword

nonn

Author

R. H. Hardin, Nov 26 2014

Status

approved