A241964 T(n,k)=Number of length n+3 0..k arrays with no consecutive four elements summing to more than 2*k

11, 50, 19, 150, 124, 33, 355, 486, 311, 57, 721, 1421, 1597, 775, 97, 1316, 3437, 5778, 5211, 1895, 166, 2220, 7280, 16660, 23320, 16649, 4663, 285, 3525, 13980, 40978, 80132, 92037, 53553, 11518, 489, 5335, 24897, 89622, 228826, 376559, 365810

Offset

1,1

Comments

Table starts

..11....50....150.....355.....721.....1316......2220......3525.......5335

..19...124....486....1421....3437.....7280.....13980.....24897......41767

..33...311...1597....5778...16660....40978.....89622....179079.....333091

..57...775...5211...23320...80132...228826....569874...1277427....2634115

..97..1895..16649...92037..376559..1247602...3536286...8889273...20314789

.166..4663..53553..365810.1782453..6853011..22111157..62336336..157897575

.285.11518.172980.1460409.8476317.37822419.138925925.439298830.1233421948

Links

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

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2) +a(n-4) -a(n-6)

k=2: [order 17]

k=3: [order 44]

k=4: [order 85]

Empirical for row n:

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

n=2: a(n) = (23/60)*n^5 + (9/4)*n^4 + (21/4)*n^3 + (25/4)*n^2 + (58/15)*n + 1

n=3: [polynomial of degree 6]

n=4: [polynomial of degree 7]

n=5: [polynomial of degree 8]

n=6: [polynomial of degree 9]

n=7: [polynomial of degree 10]

Example

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

Crossrefs

Column 1 is A118647(n+3)

Column 2 is A212226

Column 3 is A212465

Row 1 is A212560(n+1)

Sequence in context: A126398 A159486 A284857 * A306425 A241406 A215728

Adjacent sequences: A241961 A241962 A241963 * A241965 A241966 A241967

Keyword

nonn,tabl

Author

R. H. Hardin, May 03 2014

Status

approved