A228461 Two-dimensional array read by antidiagonals: T(n,k) = number of arrays of maxima of three adjacent elements of some length n+2 0..k array.

2, 3, 4, 4, 9, 7, 5, 16, 22, 11, 6, 25, 50, 46, 17, 7, 36, 95, 130, 91, 27, 8, 49, 161, 295, 310, 183, 44, 9, 64, 252, 581, 821, 736, 383, 72, 10, 81, 372, 1036, 1847, 2227, 1821, 819, 117, 11, 100, 525, 1716, 3703, 5615, 6254, 4673, 1749, 189, 12, 121, 715, 2685, 6812

Offset

1,1

Comments

There are two arrays (or lists, or vectors) involved, a length n+2 array with free elements from 0..k (thus (k+1)^(n+2) of them) and an array that is being enumerated of length n, each element of the latter being the maximum of three adjacent elements of the first array.

Many different first arrays can give the same second array.

Links

R. H. Hardin, Table of n, a(n) for n = 1..1700

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-4)

k=2: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +3*a(n-4) -a(n-5) +a(n-6) +a(n-7)

k=3: [order 10]

k=4: [order 13]

k=5: [order 16]

k=6: [order 19]

k=7: [order 22]

Empirical for row n:

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

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

n=3: a(n) = (2/3)*n^3 + (5/2)*n^2 + (17/6)*n + 1

n=4: a(n) = (1/3)*n^4 + 2*n^3 + (25/6)*n^2 + (7/2)*n + 1

n=5: a(n) = (2/15)*n^5 + (7/6)*n^4 + (25/6)*n^3 + (19/3)*n^2 + (21/5)*n + 1

n=6: [polynomial of degree 6]

n=7: [polynomial of degree 7]

Example

Table starts
...2....3.....4.....5......6......7.......8.......9......10.......11.......12
...4....9....16....25.....36.....49......64......81.....100......121......144
...7...22....50....95....161....252.....372.....525.....715......946.....1222
..11...46...130...295....581...1036....1716....2685....4015.....5786.....8086
..17...91...310...821...1847...3703....6812...11721...19117....29843....44914
..27..183...736..2227...5615..12453...25096...46941...82699...138699...223224
..44..383..1821..6254..17487..42386...92430..185727..349558...623513..1063283
..72..819..4673.18394..57303.151882..357510..768231.1535578..2893605..5191407
.117.1749.12107.55285.194064.567835.1453506.3357985.7152815.14263777.26930773
Some solutions for n=4 k=4
..3....4....4....3....3....4....3....4....3....0....3....3....4....2....0....2
..0....4....1....3....2....0....2....4....1....0....3....3....1....2....0....0
..4....1....1....0....1....0....4....0....0....0....2....1....4....2....2....3
..4....0....3....3....2....0....4....2....3....1....3....1....4....0....4....3

Crossrefs

Column 1 is A005252(n+3)

Column 2 is A217878

Column 3 is A217949.

A228464 is another column.

Row 1 is A000027(n+1)

Row 2 is A000290(n+1)

Row 3 is A002412(n+1)

Row 4 is A006324(n+1)

See A217883, A217954 for similar arrays.

Sequence in context: A269537 A269678 A269467 * A267471 A268457 A244940

Adjacent sequences: A228458 A228459 A228460 * A228462 A228463 A228464

Keyword

nonn,tabl

Author

R. H. Hardin Aug 22 2013

Extensions

Edited by N. J. A. Sloane, Sep 02 2013

Status

approved