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A203938
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Number of (n+1)X3 0..5 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively
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1
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4471, 91396, 1350442, 15288484, 145455811, 1186308022, 8607173216, 56414423998, 340158722704, 1907547529456, 10054111267835, 50188065610406, 238892619282934, 1090189574059542, 4792342014793388, 20372738874767190
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 41*a(n-1) -756*a(n-2) +8092*a(n-3) -52994*a(n-4) +187938*a(n-5) -4896*a(n-6) -3516348*a(n-7) +16307630*a(n-8) -16255022*a(n-9) -144874730*a(n-10) +643954340*a(n-11) -413594286*a(n-12) -4725980688*a(n-13) +14701463915*a(n-14) +3206495241*a(n-15) -107845952727*a(n-16) +181392027153*a(n-17) +318997719378*a(n-18) -1504214506712*a(n-19) +649644395320*a(n-20) +6192363987604*a(n-21) -11041884592111*a(n-22) -11890100719013*a(n-23) +56590394403028*a(n-24) -18867865715200*a(n-25) -173771210864807*a(n-26) +230277285039455*a(n-27) +313919995022182*a(n-28) -931823570221688*a(n-29) -76836755864653*a(n-30) +2435097165126919*a(n-31) -1622955595485466*a(n-32) -4410192209123244*a(n-33) +6456444761648337*a(n-34) +4918443565399489*a(n-35) -15496959555301252*a(n-36) -135682027406268*a(n-37) +27120842590118366*a(n-38) -13905977541311120*a(n-39) -35750398447563310*a(n-40) +37670182875491098*a(n-41) +33740169243679502*a(n-42) -65261268209963804*a(n-43) -16470665337966139*a(n-44) +85846959284662959*a(n-45) -12957902945880108*a(n-46) -89729638897851620*a(n-47) +44001785808789219*a(n-48) +74782058471680699*a(n-49) -64639011844488028*a(n-50) -47883893613059550*a(n-51) +68524253055606866*a(n-52) +20210726426572810*a(n-53) -57784407645802933*a(n-54) -484615133009475*a(n-55) +40041365168701250*a(n-56) -8694893553569570*a(n-57) -23006955574010142*a(n-58) +9854574619742212*a(n-59) +10888438912464061*a(n-60) -7252321976505707*a(n-61) -4128422661734826*a(n-62) +4135002596993622*a(n-63) +1156681702309747*a(n-64) -1922496424850251*a(n-65) -167019988903534*a(n-66) +742465422456294*a(n-67) -44901526708563*a(n-68) -239221100605037*a(n-69) +44679941474363*a(n-70) +63979480384033*a(n-71) -19746407685096*a(n-72) -13990928766934*a(n-73) +6215462339353*a(n-74) +2423314770365*a(n-75) -1519275568746*a(n-76) -308916695820*a(n-77) +295237531508*a(n-78) +22460125850*a(n-79) -45616219880*a(n-80) +929333814*a(n-81) +5520093831*a(n-82) -555675777*a(n-83) -506857657*a(n-84) +88974409*a(n-85) +33252495*a(n-86) -8622601*a(n-87) -1363978*a(n-88) +536568*a(n-89) +20508*a(n-90) -19892*a(n-91) +792*a(n-92) +336*a(n-93) -32*a(n-94) for n>98
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EXAMPLE
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Some solutions for n=4
..5..5..5....3..0..4....4..5..5....5..3..3....1..2..1....1..4..1....1..5..4
..5..5..5....0..5..3....5..5..5....3..5..5....3..2..5....5..2..5....4..4..5
..5..5..5....4..3..5....5..5..5....3..5..5....3..4..5....2..5..4....4..4..5
..5..5..5....2..5..3....5..5..5....4..5..5....4..4..5....5..4..5....3..5..4
..5..5..5....4..3..5....5..5..5....5..5..5....3..5..4....4..5..4....4..4..5
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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