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A229012
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T(n,k) = number of arrays of median of three adjacent elements of some length n+2 0..k array, with no adjacent equal elements in the latter.
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12
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2, 3, 2, 4, 7, 2, 5, 14, 15, 2, 6, 23, 46, 31, 2, 7, 34, 101, 130, 57, 2, 8, 47, 186, 359, 332, 105, 2, 9, 62, 307, 794, 1145, 830, 193, 2, 10, 79, 470, 1527, 3002, 3527, 2054, 353, 2, 11, 98, 681, 2666, 6635, 10860, 10735, 5108, 653, 2, 12, 119, 946, 4335, 13040, 27379
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OFFSET
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1,1
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COMMENTS
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Table starts
.2...3.....4......5......6.......7.......8........9.......10.......11........12
.2...7....14.....23.....34......47......62.......79.......98......119.......142
.2..15....46....101....186.....307.....470......681......946.....1271......1662
.2..31...130....359....794....1527....2666.....4335.....6674.....9839.....14002
.2..57...332...1145...3002....6635...13040....23515....39698....63605.....97668
.2.105...830...3527..10860...27379...60180...119653...220318...381749....629586
.2.193..2054..10735..38768..111311..273124...597477..1197190..2238005...3954490
.2.353..5108..32907.139456..456029.1248872..3004839..6549040.13200731..24974126
.2.653.12790.101635.506236.1888383.5780144.15315095.36345246.79063593.160271154
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: [order 13]
k=3: [order 27]
k=4: [order 46]
k=5: [order 69]
k=6: [order 95] for n>97
Empirical for row n:
n=1: a(n) = 1*n + 1
n=2: a(n) = 1*n^2 + 2*n - 1
n=3: a(n) = 1*n^3 + 3*n^2 - 3*n + 1
n=4: a(n) = (2/3)*n^4 + (10/3)*n^3 - (5/3)*n^2 + (2/3)*n - 1
n=5: [polynomial of degree 5]
n=6: [polynomial of degree 6]
n=7: [polynomial of degree 7]
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EXAMPLE
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Some solutions for n=4 k=4
..1....1....0....3....4....1....2....3....2....3....3....1....1....0....2....2
..4....1....1....1....3....0....2....1....0....0....2....3....4....4....0....1
..0....1....3....3....3....2....0....1....4....2....2....4....1....1....3....3
..3....2....3....1....0....0....1....3....3....1....0....3....4....4....2....3
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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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