A219812 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX4 array

10, 28, 165, 648, 2237, 7689, 27340, 97483, 336348, 1107489, 3485470, 10546240, 30830180, 87358002, 240482830, 644448160, 1684320795, 4300660348, 10743976755, 26294223619, 63107214528, 148665918680, 344032752665, 782623819472

Offset

1,1

Comments

Column 4 of A219816

Links

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

Formula

Empirical: a(n) = (1/109157555478267925364736000000)*n^29 - (1/342186694289241145344000000)*n^28 + (787/1613165844506422542336000000)*n^27 - (28121/537721948168807514112000000)*n^26 + (3139/811043662396391424000000)*n^25 - (1615309/8272645356443192524800000)*n^24 + (1502119/262029490928064921600000)*n^23 + (2731711/193673971555526246400000)*n^22 - (374857117/32698202989894041600000)*n^21 + (21372946241/32698202989894041600000)*n^20 - (2424466906801/119893410962944819200000)*n^19 + (493103170643/1720958052099686400000)*n^18 + (1734777644986229/344535802030357217280000)*n^17 - (40560447275480497/101334059420693299200000)*n^16 + (18007187160284767/1608477133661798400000)*n^15 - (2403356207292032407/14476294202956185600000)*n^14 + (459337879747512641/1051696587394252800000)*n^13 + (191722386943534913803/4732634643274137600000)*n^12 - (2307514571726310091297/2200840585858252800000)*n^11 + (5045165283615493010633/366806764309708800000)*n^10 - (916210841628863901264941/9917653480390656000000)*n^9 - (11218991275944388882181/94612855873536000000)*n^8 + (62417285070941262690542939/6336278612471808000000)*n^7 - (1010263806187535882917039801/8976394701001728000000)*n^6 + (48281626803788599623807524761/68070993149263104000000)*n^5 - (574880107896908134801205293/226903310497543680000)*n^4 + (17077169474218343729849/5512714054848000)*n^3 + (8439129780213343969333/643149973065600)*n^2 - (47260139138269946039/776363187600)*n + 79013201 for n>12

Example

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

Crossrefs

Sequence in context: A264579 A003665 A332432 * A345725 A185985 A358986

Adjacent sequences: A219809 A219810 A219811 * A219813 A219814 A219815

Keyword

nonn

Author

R. H. Hardin Nov 28 2012

Status

approved