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A251969
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Number of (n+1)X(2+1) 0..3 arrays with nondecreasing sum of every two consecutive values in every row and column
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1
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1600, 20000, 250000, 1750000, 12250000, 60025000, 294122500, 1129430400, 4337012736, 13940398080, 44808422400, 125737920000, 352836000000, 889440750000, 2242131890625, 5181815925000, 11975752360000, 25758754621600
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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) = 2*a(n-1) +16*a(n-2) -34*a(n-3) -119*a(n-4) +272*a(n-5) +544*a(n-6) -1360*a(n-7) -1700*a(n-8) +4760*a(n-9) +3808*a(n-10) -12376*a(n-11) -6188*a(n-12) +24752*a(n-13) +7072*a(n-14) -38896*a(n-15) -4862*a(n-16) +48620*a(n-17) -48620*a(n-19) +4862*a(n-20) +38896*a(n-21) -7072*a(n-22) -24752*a(n-23) +6188*a(n-24) +12376*a(n-25) -3808*a(n-26) -4760*a(n-27) +1700*a(n-28) +1360*a(n-29) -544*a(n-30) -272*a(n-31) +119*a(n-32) +34*a(n-33) -16*a(n-34) -2*a(n-35) +a(n-36)
Empirical for n mod 2 = 0: a(n) = (1/195689447424)*n^18 + (17/32614907904)*n^17 + (203/8153726976)*n^16 + (377/509607936)*n^15 + (31231/2038431744)*n^14 + (239305/1019215872)*n^13 + (2108695/764411904)*n^12 + (808981/31850496)*n^11 + (47324495/254803968)*n^10 + (138392485/127401984)*n^9 + (162166271/31850496)*n^8 + (75927689/3981312)*n^7 + (84551699/1492992)*n^6 + (21804659/165888)*n^5 + (3221599/13824)*n^4 + (65735/216)*n^3 + (3305/12)*n^2 + 154*n + 40
Empirical for n mod 2 = 1: a(n) = (1/195689447424)*n^18 + (17/32614907904)*n^17 + (1627/65229815808)*n^16 + (337/452984832)*n^15 + (252719/16307453952)*n^14 + (650633/2717908992)*n^13 + (139013113/48922361856)*n^12 + (108024043/4076863488)*n^11 + (6416896093/32614907904)*n^10 + (2123295587/1811939328)*n^9 + (183000365333/32614907904)*n^8 + (29276989709/1358954496)*n^7 + (3220556174161/48922361856)*n^6 + (1287371473955/8153726976)*n^5 + (526642267375/1811939328)*n^4 + (179477108125/452984832)*n^3 + (909776415625/2415919104)*n^2 + (29884946875/134217728)*n + (16544390625/268435456)
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EXAMPLE
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Some solutions for n=2
..0..0..2....1..1..1....0..1..2....0..0..1....1..2..3....0..1..2....2..1..2
..0..3..3....0..1..2....0..1..2....1..3..2....1..0..3....3..0..3....1..3..1
..2..2..3....2..2..2....2..1..3....2..2..3....3..2..3....0..3..2....3..3..3
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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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