A250140 T(n,k)=Number of length n+2 0..k arrays with the medians of every three consecutive terms nondecreasing

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

R. H. Hardin, Table of n, a(n) for n = 1..9999

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

Adjacent sequences: A250137 A250138 A250139 * A250141 A250142 A250143

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 13 2014

Status

approved