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A250140
T(n,k)=Number of length n+2 0..k arrays with the medians of every three consecutive terms nondecreasing
13
8, 27, 14, 64, 67, 24, 125, 204, 162, 41, 216, 485, 632, 391, 68, 343, 986, 1827, 1959, 900, 111, 512, 1799, 4368, 6902, 5696, 2026, 180, 729, 3032, 9156, 19446, 24125, 16104, 4530, 289, 1000, 4809, 17424, 46914, 79200, 81664, 45232, 9975, 460, 1331
OFFSET
1,1
COMMENTS
Table starts
...8....27.....64.....125......216.......343........512........729........1000
..14....67....204.....485......986......1799.......3032.......4809........7270
..24...162....632....1827.....4368......9156......17424......30789.......51304
..41...391...1959....6902....19446.....46914.....100962.....199023......365959
..68...900...5696...24125....79200....217856.....526032....1149057.....2318140
.111..2026..16104...81664...311498....974944....2637228....6376143....14100493
.180..4530..45232..274901..1219944...4350588...13201680...35373129....85849852
.289..9975.124249..899306..4617079..18667931...63266403..187131076...496682670
.460.21694.335328.2878124.17036428..77880418..294117016..958537837..2777976392
.728.46871.897523.9128858.62297886.322089271.1356124591.4872648817.15429444696
LINKS
FORMULA
Empirical for column k, apparently a recurrence of order 7*k-1:
k=1: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -2*a(n-4) -a(n-6)
k=2: [order 13]
k=3: [order 20]
k=4: [order 27]
k=5: [order 34]
k=6: [order 41]
k=7: [order 48]
Empirical for row n, apparently a polynomial of degree n+2:
n=1: a(n) = n^3 + 3*n^2 + 3*n + 1
n=2: a(n) = (2/3)*n^4 + (10/3)*n^3 + (16/3)*n^2 + (11/3)*n + 1
n=3: a(n) = (13/30)*n^5 + 3*n^4 + (22/3)*n^3 + 8*n^2 + (127/30)*n + 1
n=4: [polynomial of degree 6]
n=5: [polynomial of degree 7]
n=6: [polynomial of degree 8]
n=7: [polynomial of degree 9]
EXAMPLE
Some solutions for n=5 k=4
..4....0....3....2....2....0....1....2....3....0....0....1....0....0....2....3
..0....2....3....4....3....1....3....3....0....2....2....3....0....3....4....2
..4....1....2....2....0....1....4....1....0....0....0....1....1....4....2....2
..4....3....3....3....2....2....1....2....1....1....3....1....3....4....0....0
..1....2....3....4....2....1....3....3....0....1....2....3....0....0....4....3
..4....3....2....2....4....4....3....4....2....4....0....1....3....4....4....4
..4....4....4....3....4....2....3....4....3....0....3....1....3....4....2....0
CROSSREFS
Column 1 is A164406(n+2) for n>1
Row 1 is A000578(n+1)
Sequence in context: A367934 A053149 A102637 * A070510 A224787 A361264
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 13 2014
STATUS
approved