A228740 T(n,k) = number of arrays of the median of three adjacent elements of some length n+2 0..k array.

2, 3, 4, 4, 9, 8, 5, 16, 27, 16, 6, 25, 64, 77, 28, 7, 36, 125, 232, 185, 50, 8, 49, 216, 545, 696, 447, 88, 9, 64, 343, 1096, 1943, 2072, 1071, 156, 10, 81, 512, 1981, 4504, 6797, 6130, 2593, 278, 11, 100, 729, 3312, 9191, 17986, 23627, 18378, 6333, 496, 12, 121

Offset: 1

Author

R. H. Hardin Sep 01 2013

Keywords

• nonn
• tabl

Comments

See A228461 for more information about the definition. - N. J. A. Sloane, Sep 02 2013

Table starts

...2....3.....4......5.......6.......7........8........9.......10........11

...4....9....16.....25......36......49.......64.......81......100.......121

...8...27....64....125.....216.....343......512......729.....1000......1331

..16...77...232....545....1096....1981.....3312.....5217.....7840.....11341

..28..185...696...1943....4504....9191....17088....29589....48436.....75757

..50..447..2072...6797...17986...41083....84288...159321...282274....474551

..88.1071..6130..23627...71278..181885...410828...845517..1617004...2913955

.156.2593.18378..83391..287154..819099..2037214..4564455..9418762..18182967

.278.6333.55716.298239.1174282.3749921.10282648.25107493.55950398.115793733

Examples

			Some solutions for n=4 k=4
..1..4..3..2..0..4..2..2..4..1..2..0..0..0..2..1
..2..0..2..0..0..3..3..4..2..2..2..1..2..2..3..4
..1..3..0..0..0..1..0..1..3..1..0..0..2..3..4..4
..3..1..2..1..4..1..1..4..1..2..4..0..2..2..3..3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..811

Crossrefs

Row 1 is A000027(n+1)

Row 2 is A000290(n+1)

Row 3 is A000578(n+1)

For other rows, columns and diagonals see A228739-A228744.

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) -a(n-3) +a(n-5)

k=2: [order 14]

k=3: [order 26]

k=4: [order 43]

Empirical for row n:

n=1: a(n) = n + 1

n=2: a(n) = n^2 + 2*n + 1

n=3: a(n) = n^3 + 3*n^2 + 3*n + 1

n=4: a(n) = (2/3)*n^4 + 4*n^3 + (19/3)*n^2 + 4*n + 1

n=5: [polynomial of degree 5]

n=6: [polynomial of degree 6]

n=7: [polynomial of degree 7]