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Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 3Xn array
1

%I #4 Dec 01 2012 18:00:42

%S 20,76,368,2070,8523,30558,100761,313108,921941,2585664,6949146,

%T 18004266,45195087,110356035,262913226,612588113,1398558018,

%U 3133356168,6897689403,14935630967,31839486936,66877133838,138505092333,283012794327

%N Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 3Xn array

%C Row 3 of A219939

%H R. H. Hardin, <a href="/A219941/b219941.txt">Table of n, a(n) for n = 1..143</a>

%F Empirical: a(n) = (1/403291461126605635584000000)*n^26 + (1/4431774298094567424000000)*n^25 - (1/41363226782215962624000)*n^24 + (197/620448401733239439360000)*n^23 + (1217/8174550747473510400000)*n^22 - (256279/24523652242420531200000)*n^21 + (65279/408727537373675520000)*n^20 + (1856273/87584472294359040000)*n^19 - (653349821/430239513024921600000)*n^18 + (54055377587/1290718539074764800000)*n^17 + (2320366871/27839027313377280000)*n^16 - (3717812638987/83517081940131840000)*n^15 + (5484808764935099/3619073550739046400000)*n^14 - (2496111855647623/119310117057331200000)*n^13 - (72022776713071/632705166213120000)*n^12 + (37557787492220189/3796230997278720000)*n^11 - (2181011993923982069/13444984782028800000)*n^10 + (27307415379539594171/80669908692172800000)*n^9 + (1343328329294561945371/38318206628782080000)*n^8 - (2841881108865735917063/3649353012264960000)*n^7 + (1799819148808436831247773/195139015239168000000)*n^6 - (3401216027548345002782833/48784753809792000000)*n^5 + (46648398935022032997047/138524609583360000)*n^4 - (7212118970409085627577/7792009289064000)*n^3 + (9943478169830685757/12528895579200)*n^2 + (4275677919744929/1912224600)*n - 4212297 for n>13

%e Some solutions for n=3

%e ..2..0..1....1..1..2....2..2..2....1..1..1....3..0..0....2..2..2....2..0..2

%e ..3..0..0....1..0..1....3..3..2....1..1..1....3..3..3....2..2..2....3..0..0

%e ..3..0..0....2..0..0....3..3..3....2..1..1....3..3..3....3..2..2....3..0..0

%K nonn

%O 1,1

%A _R. H. Hardin_ Dec 01 2012

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Last modified September 19 21:59 EDT 2024. Contains 376015 sequences. (Running on oeis4.)