A212835 T(n,k)=Number of 0..k arrays of length n+1 with 0 never adjacent to k

2, 7, 2, 14, 17, 2, 23, 50, 41, 2, 34, 107, 178, 99, 2, 47, 194, 497, 634, 239, 2, 62, 317, 1106, 2309, 2258, 577, 2, 79, 482, 2137, 6306, 10727, 8042, 1393, 2, 98, 695, 3746, 14407, 35954, 49835, 28642, 3363, 2, 119, 962, 6113, 29114, 97127, 204994, 231521

Offset

1,1

Comments

Table starts

.2.....7......14.......23........34.........47.........62..........79

.2....17......50......107.......194........317........482.........695

.2....41.....178......497......1106.......2137.......3746........6113

.2....99.....634.....2309......6306......14407......29114.......53769

.2...239....2258....10727.....35954......97127.....226274......472943

.2...577....8042....49835....204994.....654797....1758602.....4159927

.2..1393...28642...231521...1168786....4414417...13667858....36590017

.2..3363..102010..1075589...6663906...29760487..106226618...321839625

.2..8119..363314..4996919..37994674..200635007..825593474..2830847119

.2.19601.1293962.23214443.216628994.1352612477.6416514026.24899654327

Links

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

Formula

Empirical for column k: a(n) = k*a(n-1) +(k-1)*a(n-2)

Empirical for rows:

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

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

n=3: a(k) = k^4 + 4*k^3 - 4*k + 1

n=4: a(k) = k^5 + 5*k^4 + 2*k^3 - 8*k^2 + k + 1

n=5: a(k) = k^6 + 6*k^5 + 5*k^4 - 12*k^3 - 3*k^2 + 6*k - 1

n=6: a(k) = k^7 + 7*k^6 + 9*k^5 - 15*k^4 - 13*k^3 + 15*k^2 - k - 1

n=7: a(k) = k^8 + 8*k^7 + 14*k^6 - 16*k^5 - 30*k^4 + 24*k^3 + 8*k^2 - 8*k + 1

Example

Some solutions for n=5 k=4
..1....4....1....1....1....3....2....1....1....4....3....1....0....2....2....3
..1....3....0....4....2....4....1....1....2....2....3....4....1....3....3....1
..1....3....3....1....3....3....2....2....2....4....3....3....1....1....0....3
..1....3....0....4....2....3....3....3....4....2....2....0....4....4....2....1
..1....4....0....3....2....2....3....3....4....4....0....1....4....3....4....2
..1....2....0....4....3....1....0....2....4....2....3....2....1....4....3....4

Crossrefs

Column 2 is A001333(n+2)

Column 3 is A055099(n+1)

Column 4 is A126473(n+1)

Column 5 is A126501(n+1)

Column 6 is A126528(n+1)

Row 1 is A008865(n+1)

Sequence in context: A222853 A222654 A318059 * A089123 A281751 A282366

Adjacent sequences: A212832 A212833 A212834 * A212836 A212837 A212838

Keyword

nonn,tabl

Author

R. H. Hardin May 28 2012

Status

approved