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A259006
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T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock sum of the two medians of the central row and column plus the two sums of the diagonal and antidiagonal nondecreasing horizontally, vertically and ne-to-sw antidiagonally
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14
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512, 2444, 2444, 9374, 6271, 9374, 34698, 18341, 21073, 34698, 113474, 50654, 55760, 59549, 113474, 330684, 131557, 159480, 116098, 130296, 330684, 914320, 317141, 397152, 225215, 142316, 263417, 914320, 2433544, 701282, 915452, 402742, 177118
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OFFSET
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1,1
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COMMENTS
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Table starts
......512....2444...9374..34698.113474.330684..914320.2433544.6176662.15093057
.....2444....6271..18341..50654.131557.317141..701282.1467387.2896645..5442921
.....9374...21073..55760.159480.397152.915452.2005182.4136140.8078000.15207697
....34698...59549.116098.225215.402742.780329.1284465.2218382.3724801..6307988
...113474..130296.142316.177118.219424.321144..431280..628483..873376..1362527
...330684..263417.191035.174655.210946.292814..390714..533771..758616..1186813
...914320..459014.134036..49839..35404..49717...73734..133352..251774...493203
..2433544..746902.138255..44035..30072..42876...61001..112980..214950...418576
..6176662.1157855.135282..31798..23070..35111...59336..109259..204210...388170
.15093057.1747626.125066..31346..28125..36146...60827..109221..200940...373950
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LINKS
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FORMULA
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Empirical for column k:
k=1: [linear recurrence of order 68] for n>70
k=2: [order 46] for n>60
k=3: [order 22] for n>36
k=4: a(n) = 2*a(n-1) -a(n-2) +a(n-12) -2*a(n-13) +a(n-14) for n>27
k=5: a(n) = a(n-1) +a(n-12) -a(n-13) for n>23
k=6: a(n) = a(n-1) +a(n-12) -a(n-13) for n>24
k=7: a(n) = a(n-1) +a(n-12) -a(n-13) for n>25
Empirical quasipolynomials for column k:
k=3: quasipolynomial of degree 2 with period 60 for n>14
k=4: polynomial of degree 2 plus a quasipolynomial of degree 0 with period 12 for n>13
k=5: polynomial of degree 1 plus a quasipolynomial of degree 0 with period 12 for n>10
k=6: polynomial of degree 1 plus a quasipolynomial of degree 0 with period 12 for n>11
k=7: polynomial of degree 1 plus a quasipolynomial of degree 0 with period 12 for n>12
Empirical for row n:
n=1: [linear recurrence of order 68] for n>70
n=2: [order 64] for n>82
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EXAMPLE
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Some solutions for n=3 k=4
..0..1..0..1..1..1....1..1..0..1..0..0....0..0..0..1..0..0....0..1..0..0..1..0
..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....1..0..0..0..0..1
..0..1..1..1..1..1....0..0..1..0..1..1....0..0..0..0..1..0....1..1..1..1..1..1
..0..1..0..1..1..0....1..0..1..0..1..0....0..1..1..1..1..0....0..1..0..1..1..0
..0..1..1..1..0..1....1..1..1..1..1..0....1..0..0..1..1..1....0..1..1..1..0..1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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