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%I #4 Nov 22 2014 22:25:37
%S 22500,787500,27562500,450187500,7353062500,74118870000,747118209600,
%T 5379251109120,38730607985664,217365657062400,1219909299840000,
%U 5648304538800000,26152226372250000,103882454756437500
%N Number of (n+1)X(6+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column
%C Column 6 of A250443
%H R. H. Hardin, <a href="/A250441/b250441.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +26*a(n-2) -54*a(n-3) -324*a(n-4) +702*a(n-5) +2574*a(n-6) -5850*a(n-7) -14625*a(n-8) +35100*a(n-9) +63180*a(n-10) -161460*a(n-11) -215280*a(n-12) +592020*a(n-13) +592020*a(n-14) -1776060*a(n-15) -1332045*a(n-16) +4440150*a(n-17) +2466750*a(n-18) -9373650*a(n-19) -3749460*a(n-20) +16872570*a(n-21) +4601610*a(n-22) -26075790*a(n-23) -4345965*a(n-24) +34767720*a(n-25) +2674440*a(n-26) -40116600*a(n-27) +40116600*a(n-29) -2674440*a(n-30) -34767720*a(n-31) +4345965*a(n-32) +26075790*a(n-33) -4601610*a(n-34) -16872570*a(n-35) +3749460*a(n-36) +9373650*a(n-37) -2466750*a(n-38) -4440150*a(n-39) +1332045*a(n-40) +1776060*a(n-41) -592020*a(n-42) -592020*a(n-43) +215280*a(n-44) +161460*a(n-45) -63180*a(n-46) -35100*a(n-47) +14625*a(n-48) +5850*a(n-49) -2574*a(n-50) -702*a(n-51) +324*a(n-52) +54*a(n-53) -26*a(n-54) -2*a(n-55) +a(n-56)
%F Empirical for n mod 2 = 0: a(n) = (1/46168933054965350400)*n^28 + (23/5771116631870668800)*n^27 + (451/1282470362637926400)*n^26 + (19057/961852771978444800)*n^25 + (770023/961852771978444800)*n^24 + (1485127/60115798248652800)*n^23 + (48523211/80154397664870400)*n^22 + (26923657/2226511046246400)*n^21 + (12056968741/60115798248652800)*n^20 + (4207062883/1502894956216320)*n^19 + (498997793059/15028949562163200)*n^18 + (1266437177191/3757237390540800)*n^17 + (11060075878277/3757237390540800)*n^16 + (2605379422429/117413668454400)*n^15 + (5434788716347/37572373905408)*n^14 + (191574384904933/234827336908800)*n^13 + (233506669475617/58706834227200)*n^12 + (245496100146481/14676708556800)*n^11 + (665395240637933/11007531417600)*n^10 + (102760865752237/550376570880)*n^9 + (112182743639143/229323571200)*n^8 + (20566195851937/19110297600)*n^7 + (1561209722213/796262400)*n^6 + (19261940849/6635520)*n^5 + (4701106061/1382400)*n^4 + (34907687/11520)*n^3 + (185039/96)*n^2 + (3115/4)*n + 150
%F Empirical for n mod 2 = 1: a(n) = (1/46168933054965350400)*n^28 + (23/5771116631870668800)*n^27 + (325/923378661099307008)*n^26 + (114641/5771116631870668800)*n^25 + (37156691/46168933054965350400)*n^24 + (71922841/2885558315935334400)*n^23 + (7082252513/11542233263741337600)*n^22 + (35566445347/2885558315935334400)*n^21 + (9501813256121/46168933054965350400)*n^20 + (16707362824109/5771116631870668800)*n^19 + (159961807233959/4616893305496535040)*n^18 + (82028427321371/230844665274826752)*n^17 + (144932272992586787/46168933054965350400)*n^16 + (34583558049937571/1442779157967667200)*n^15 + (914775351038608423/5771116631870668800)*n^14 + (1310460363060759641/1442779157967667200)*n^13 + (208068829025881411739/46168933054965350400)*n^12 + (111506687915337527297/5771116631870668800)*n^11 + (1646408524090171699187/23084466527482675200)*n^10 + (433736506410530367917/1923705543956889600)*n^9 + (345394097513574221281/569986827839078400)*n^8 + (29299006250741638439/21374506043965440)*n^7 + (14674937650257198937/5699868278390784)*n^6 + (207995809091667065/52776558133248)*n^5 + (1347860673706015875/281474976710656)*n^4 + (156248550749725875/35184372088832)*n^3 + (415361160772543125/140737488355328)*n^2 + (44019729622378125/35184372088832)*n + (71508843479390625/281474976710656)
%e Some solutions for n=1
%e ..0..0..0..0..1..1..2....2..0..2..0..2..2..2....0..0..0..1..0..1..2
%e ..0..0..0..1..1..2..1....0..1..1..2..2..2..2....0..2..2..2..2..2..2
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 22 2014
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