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 A250442 Number of (n+1)X(7+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column 1

%I

%S 50625,2480625,121550625,2647102500,57648010000,747118209600,

%T 9682651996416,87143867967744,784294811709696,5379800012294400,

%U 36902256320160000,205033454758440000,1139190980775210000

%N Number of (n+1)X(7+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column

%C Column 7 of A250443

%H R. H. Hardin, <a href="/A250442/b250442.txt">Table of n, a(n) for n = 1..170</a>

%F Empirical: a(n) = 2*a(n-1) +30*a(n-2) -62*a(n-3) -434*a(n-4) +930*a(n-5) +4030*a(n-6) -8990*a(n-7) -26970*a(n-8) +62930*a(n-9) +138446*a(n-10) -339822*a(n-11) -566370*a(n-12) +1472562*a(n-13) +1893294*a(n-14) -5259150*a(n-15) -5259150*a(n-16) +15777450*a(n-17) +12271350*a(n-18) -40320150*a(n-19) -24192090*a(n-20) +88704330*a(n-21) +40320150*a(n-22) -169344630*a(n-23) -56448210*a(n-24) +282241050*a(n-25) +65132550*a(n-26) -412506150*a(n-27) -58929450*a(n-28) +530365050*a(n-29) +35357670*a(n-30) -601080390*a(n-31) +601080390*a(n-33) -35357670*a(n-34) -530365050*a(n-35) +58929450*a(n-36) +412506150*a(n-37) -65132550*a(n-38) -282241050*a(n-39) +56448210*a(n-40) +169344630*a(n-41) -40320150*a(n-42) -88704330*a(n-43) +24192090*a(n-44) +40320150*a(n-45) -12271350*a(n-46) -15777450*a(n-47) +5259150*a(n-48) +5259150*a(n-49) -1893294*a(n-50) -1472562*a(n-51) +566370*a(n-52) +339822*a(n-53) -138446*a(n-54) -62930*a(n-55) +26970*a(n-56) +8990*a(n-57) -4030*a(n-58) -930*a(n-59) +434*a(n-60) +62*a(n-61) -30*a(n-62) -2*a(n-63) +a(n-64)

%F Empirical for n mod 2 = 0: a(n) = (1/295481171551778242560000)*n^32 + (7/9233786610993070080000)*n^31 + (7/85498024175861760000)*n^30 + (5243/923378661099307008000)*n^29 + (262369/923378661099307008000)*n^28 + (1401743/128247036263792640000)*n^27 + (3233819/9618527719784448000)*n^26 + (816965149/96185277197844480000)*n^25 + (1279779727/7124835347988480000)*n^24 + (77545763309/24046319299461120000)*n^23 + (298628314543/6011579824865280000)*n^22 + (442084983011/667953313873920000)*n^21 + (46132907907427/6011579824865280000)*n^20 + (116909942540279/1502894956216320000)*n^19 + (802092891287/1159641169920000)*n^18 + (2031366183004879/375723739054080000)*n^17 + (55903810241301923/1502894956216320000)*n^16 + (261298569894229/1159641169920000)*n^15 + (84611785049939939/70448201072640000)*n^14 + (99060914744459353/17612050268160000)*n^13 + (7528886885201117/326149079040000)*n^12 + (91063559073748373/1100753141760000)*n^11 + (70894521213893131/275188285440000)*n^10 + (5294479580641027/7644119040000)*n^9 + (12186324387089641/7644119040000)*n^8 + (24741813694283/7962624000)*n^7 + (16771060400671/3317760000)*n^6 + (93056990999/13824000)*n^5 + (658151479/92160)*n^4 + (1113469/192)*n^3 + (54115/16)*n^2 + 1260*n + 225

%F Empirical for n mod 2 = 1: a(n) = (1/295481171551778242560000)*n^32 + (7/9233786610993070080000)*n^31 + (1513/18467573221986140160000)*n^30 + (10507/1846757322198614016000)*n^29 + (10537219/36935146443972280320000)*n^28 + (101613407/9233786610993070080000)*n^27 + (1254630283/3693514644397228032000)*n^26 + (79578454319/9233786610993070080000)*n^25 + (13531572555887/73870292887944560640000)*n^24 + (30546647311187/9233786610993070080000)*n^23 + (37898002769801/738702928879445606400)*n^22 + (6360093759255299/9233786610993070080000)*n^21 + (297518478101705581/36935146443972280320000)*n^20 + (761220098616092507/9233786610993070080000)*n^19 + (2736237844091525131/3693514644397228032000)*n^18 + (54099304221246858539/9233786610993070080000)*n^17 + (6032326528400394272179/147740585775889121280000)*n^16 + (2316199055347180883957/9233786610993070080000)*n^15 + (5014841998373251341143/3693514644397228032000)*n^14 + (59703913143687617298949/9233786610993070080000)*n^13 + (998160378663138824821829/36935146443972280320000)*n^12 + (60812335346478039487891/615585774066204672000)*n^11 + (71663362568569460507117/227994731135631360000)*n^10 + (295828034292591834286967/341992096703447040000)*n^9 + (1862331872171523328148239/911978924542525440000)*n^8 + (10363813651198361679941/2533274790395904000)*n^7 + (772024515761134222363/112589990684262400)*n^6 + (106193495738755717173/11258999068426240)*n^5 + (93356331606752896395/9007199254740992)*n^4 + (19692809375944600665/2251799813685248)*n^3 + (23948041990752512325/4503599627370496)*n^2 + (4668342475512263625/2251799813685248)*n + (28034326997660300625/72057594037927936)

%e Some solutions for n=1

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 22 2014

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Last modified July 6 15:30 EDT 2022. Contains 355110 sequences. (Running on oeis4.)