A268457 T(n,k)=Number of length-n 0..k arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.

2, 3, 4, 4, 9, 7, 5, 16, 25, 11, 6, 25, 61, 67, 16, 7, 36, 121, 229, 176, 22, 8, 49, 211, 581, 852, 456, 29, 9, 64, 337, 1231, 2776, 3146, 1169, 37, 10, 81, 505, 2311, 7160, 13204, 11536, 2971, 46, 11, 100, 721, 3977, 15816, 41526, 62535, 42032, 7496, 56, 12, 121

Offset: 1

Author

R. H. Hardin, Feb 04 2016

Keywords

• nonn
• tabl

Comments

Table starts

..2.....3......4.......5........6.........7.........8..........9.........10

..4.....9.....16......25.......36........49........64.........81........100

..7....25.....61.....121......211.......337.......505........721........991

.11....67....229.....581.....1231......2311......3977.......6409.......9811

.16...176....852....2776.....7160.....15816.....31276......56912......97056

.22...456...3146...13204....41526....108032....245626.....504876.....959414

.29..1169..11536...62535...240170....736525...1926444....4474451....9476950

.37..2971..42032..294967..1385338...5012171..15089356...39616567...93543782

.46..7496.152254.1385969..7970326..34047931.118040270..350431909..922677334

.56.18796.548568.6488635.45742764.230889543.922247248.3096903363.9094484100

Examples

			Some solutions for n=6 k=4
..3....2....3....2....2....0....4....2....2....0....1....0....0....3....4....3
..0....2....1....2....4....0....1....1....2....4....4....2....3....2....3....3
..0....4....1....1....4....2....3....0....1....4....2....1....1....2....0....1
..3....0....4....2....3....2....1....0....2....4....4....4....3....1....0....0
..4....1....2....3....2....2....0....4....0....4....4....4....1....3....1....3
..0....1....3....4....3....1....4....0....2....0....1....1....1....2....4....2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..421

Crossrefs

Column 1 is A000124.

Row 1 is A000027(n+1).

Row 2 is A000290(n+1).

Row 3 is A061600(n+1).

Formula

Empirical for column k:

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

k=2: a(n) = 6*a(n-1) -13*a(n-2) +14*a(n-3) -10*a(n-4) +4*a(n-5) -a(n-6)

k=3: [order 15]

k=4: [order 28]

k=5: [order 51]

k=6: [order 89]

Empirical for row n:

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

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

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

n=4: a(n) = n^4 + 4*n^3 + 4*n^2 + n + 1

n=5: a(n) = n^5 + 5*n^4 + 7*n^3 + n^2 + 2*n

n=6: a(n) = n^6 + 6*n^5 + 11*n^4 + 2*n^3 + 6*n - 4

n=7: a(n) = n^7 + 7*n^6 + 16*n^5 + 5*n^4 - 7*n^3 + 18*n^2 - 5*n - 5 for n>1