A217954 T(n,k) = number of n-element 0..3 arrays with each element the minimum of k adjacent elements of a random 0..3 array of n+k-1 elements.

4, 4, 16, 4, 16, 64, 4, 16, 50, 256, 4, 16, 50, 144, 1024, 4, 16, 50, 130, 422, 4096, 4, 16, 50, 130, 310, 1268, 16384, 4, 16, 50, 130, 296, 736, 3823, 65536, 4, 16, 50, 130, 296, 624, 1821, 11472, 262144, 4, 16, 50, 130, 296, 610, 1289, 4673, 34350, 1048576, 4, 16

Offset

1,1

Comments

See A228461 for comments on the definition. - N. J. A. Sloane, Sep 02 2013

Table starts

........4......4......4.....4.....4.....4.....4.....4.....4.....4.....4.....4

.......16.....16.....16....16....16....16....16....16....16....16....16....16

.......64.....50.....50....50....50....50....50....50....50....50....50....50

......256....144....130...130...130...130...130...130...130...130...130...130

.....1024....422....310...296...296...296...296...296...296...296...296...296

.....4096...1268....736...624...610...610...610...610...610...610...610...610

....16384...3823...1821..1289..1177..1163..1163..1163..1163..1163..1163..1163

....65536..11472...4673..2741..2209..2097..2083..2083..2083..2083..2083..2083

...262144..34350..12107..6134..4202..3670..3558..3544..3544..3544..3544..3544

..1048576.102896..31103.14269..8366..6434..5902..5790..5776..5776..5776..5776

..4194304.308419..79039.33577.17569.11666..9734..9202..9090..9076..9076..9076

.16777216.924532.199819.78304.38251.22313.16410.14478.13946.13834.13820.13820

Links

R. H. Hardin, Table of n, a(n) for n = 1..1275

Formula

Empirical for column k:

k=2: a(n) = 4*a(n-1) -6*a(n-2) +10*a(n-3) -5*a(n-4) +6*a(n-5) -a(n-6) +a(n-7)

k=3: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) +5*a(n-4) -4*a(n-5) +6*a(n-6) +4*a(n-7) +2*a(n-9) +a(n-10)

k=4: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) +6*a(n-5) -4*a(n-6) +6*a(n-7) +4*a(n-8) +5*a(n-9) +a(n-10) +3*a(n-11) +2*a(n-12) +a(n-13)

k=5: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) +6*a(n-6) -4*a(n-7) +6*a(n-8) +4*a(n-9) +5*a(n-10) +6*a(n-11) +2*a(n-12) +4*a(n-13) +3*a(n-14) +2*a(n-15) +a(n-16)

k=6: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) +6*a(n-7) -4*a(n-8) +6*a(n-9) +4*a(n-10) +5*a(n-11) +6*a(n-12) +7*a(n-13) +3*a(n-14) +5*a(n-15) +4*a(n-16) +3*a(n-17) +2*a(n-18) +a(n-19)

k=7: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) +6*a(n-8) -4*a(n-9) +6*a(n-10) +4*a(n-11) +5*a(n-12) +6*a(n-13) +7*a(n-14) +8*a(n-15) +4*a(n-16) +6*a(n-17) +5*a(n-18) +4*a(n-19) +3*a(n-20) +2*a(n-21) +a(n-22)

Diagonal: a(n) = (1/720)*n^6 + (1/48)*n^5 + (23/144)*n^4 + (9/16)*n^3 + (241/180)*n^2 + (11/12)*n + 1

Example

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

Crossrefs

Column 2 is A203094(n+1). A217949 is also a column. Cf. A228461, A217883.

Sequence in context: A255298 A255302 A102376 * A273749 A273563 A278254

Adjacent sequences: A217951 A217952 A217953 * A217955 A217956 A217957

Keyword

nonn,tabl

Author

R. H. Hardin, suggestion that the diagonal might be a polynomial from L. Edson Jeffery in the Sequence Fans Mailing List, Oct 15 2012

Status

approved