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

Author

R. H. Hardin May 28 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

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)

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