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A219855 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 4Xn array 1

%I #4 Nov 29 2012 16:45:00

%S 15,33,225,1302,5950,23946,88110,303739,996299,3134799,9509576,

%T 27911314,79482488,220049935,593073991,1557365893,3986731613,

%U 9954711223,24261060624,57756733037,134430995512,306213956668,683311240461

%N Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 4Xn array

%C Row 4 of A219852

%H R. H. Hardin, <a href="/A219855/b219855.txt">Table of n, a(n) for n = 1..150</a>

%F Empirical: a(n) = (1/4476539695045017600000)*n^25 - (1/10521781334507520000)*n^24 + (731099/34469355651846635520000)*n^23 - (31627/9859655506821120000)*n^22 + (42536399/116779296392478720000)*n^21 - (17707087/540644890705920000)*n^20 + (35134937603/14597412049059840000)*n^19 - (858456113/5820339732480000)*n^18 + (36499179417979/4780439033610240000)*n^17 - (35508053885867/105450861035520000)*n^16 + (2299252943948789/180772904632320000)*n^15 - (1266420435546319/3068675850240000)*n^14 + (45796004944005863161/3977003901911040000)*n^13 - (3520116128603007397/12746807377920000)*n^12 + (1197917853623717248663/210901722071040000)*n^11 - (1315465329075664858459/13181357629440000)*n^10 + (81681760489360582476587/54877488906240000)*n^9 - (754404910866400228157/40419025920000)*n^8 + (353892739810318116207762331/1824676506132480000)*n^7 - (62078954068811245030051031/38014093877760000)*n^6 + (4764568085262213723737372453/443497761907200000)*n^5 - (442494509961053995830154733/8558728738560000)*n^4 + (139493031467135894289315229/890515347321600)*n^3 - (865466610579163798625533/5936768982144)*n^2 - (4206940214873365983779/5354228880)*n + 2337982013816 for n>23

%e Some solutions for n=3

%e ..1..1..0....1..1..1....0..0..0....1..0..0....1..1..1....0..0..0....1..0..0

%e ..0..0..0....1..1..1....0..0..2....1..0..0....1..1..1....0..0..1....0..0..0

%e ..0..0..2....1..0..0....1..1..2....1..0..2....1..1..0....1..0..0....0..0..1

%e ..2..2..2....1..0..1....2..1..1....2..2..2....0..0..0....1..0..2....2..1..1

%K nonn

%O 1,1

%A _R. H. Hardin_ Nov 29 2012

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Last modified March 28 07:20 EDT 2024. Contains 371235 sequences. (Running on oeis4.)