A229012 T(n,k) = number of arrays of median of three adjacent elements of some length n+2 0..k array, with no adjacent equal elements in the latter.

2, 3, 2, 4, 7, 2, 5, 14, 15, 2, 6, 23, 46, 31, 2, 7, 34, 101, 130, 57, 2, 8, 47, 186, 359, 332, 105, 2, 9, 62, 307, 794, 1145, 830, 193, 2, 10, 79, 470, 1527, 3002, 3527, 2054, 353, 2, 11, 98, 681, 2666, 6635, 10860, 10735, 5108, 653, 2, 12, 119, 946, 4335, 13040, 27379

Offset: 1

Author

R. H. Hardin, Sep 10 2013

Keywords

• nonn
• tabl

Comments

Table starts

.2...3.....4......5......6.......7.......8........9.......10.......11........12

.2...7....14.....23.....34......47......62.......79.......98......119.......142

.2..15....46....101....186.....307.....470......681......946.....1271......1662

.2..31...130....359....794....1527....2666.....4335.....6674.....9839.....14002

.2..57...332...1145...3002....6635...13040....23515....39698....63605.....97668

.2.105...830...3527..10860...27379...60180...119653...220318...381749....629586

.2.193..2054..10735..38768..111311..273124...597477..1197190..2238005...3954490

.2.353..5108..32907.139456..456029.1248872..3004839..6549040.13200731..24974126

.2.653.12790.101635.506236.1888383.5780144.15315095.36345246.79063593.160271154

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..925

Crossrefs

Row 2 is A008865(n+1).

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: [order 13]

k=3: [order 27]

k=4: [order 46]

k=5: [order 69]

k=6: [order 95] for n>97

Empirical for row n:

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

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

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

n=4: a(n) = (2/3)*n^4 + (10/3)*n^3 - (5/3)*n^2 + (2/3)*n - 1

n=5: [polynomial of degree 5]

n=6: [polynomial of degree 6]

n=7: [polynomial of degree 7]