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A229012
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.
12
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
OFFSET
1,1
COMMENTS
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
LINKS
FORMULA
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]
EXAMPLE
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
CROSSREFS
Row 2 is A008865(n+1).
Sequence in context: A341098 A353330 A254967 * A207606 A303845 A132439
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Sep 10 2013
STATUS
approved