A249982 T(n,k) is the number of length n+1 0..2*k arrays with the sum of the absolute values of adjacent differences equal to n*k.

4, 6, 10, 8, 24, 20, 10, 42, 88, 64, 12, 64, 208, 384, 136, 14, 90, 426, 1242, 1606, 466, 16, 120, 728, 3030, 6856, 7138, 1012, 18, 154, 1178, 6252, 22560, 43068, 31380, 3580, 20, 192, 1744, 11524, 55372, 168506, 245860, 141272, 7864, 22, 234, 2508, 19574, 123154

Offset: 1

Author

R. H. Hardin, Nov 10 2014

Keywords

• nonn
• tabl

Examples

			Table starts:
.....4.......6........8........10.........12..........14..........16
....10......24.......42........64.........90.........120.........154
....20......88......208.......426........728........1178........1744
....64.....384.....1242......3030.......6252.......11524.......19574
...136....1606.....6856.....22560......55372......123154......237348
...466....7138....43068....168506.....508902.....1290856.....2886016
..1012...31380...245860...1293326....4598532....14027522....35380112
..3580..141272..1589346...9937894...43752328...152155572...446342246
..7864..635686..9213728..77372824..399919272..1672105528..5529256528
.28340.2890884.60568000.604180880.3872197278.18444783546.70948896558
Some solutions for n=5 k=4:
..8....5....0....8....3....7....1....0....8....1....1....1....0....0....2....4
..3....1....5....3....8....0....6....3....4....6....2....5....7....2....5....8
..8....6....3....8....0....7....3....2....8....0....6....3....1....8....7....7
..1....4....4....0....2....5....7....8....8....2....0....8....4....6....0....3
..1....8....0....1....4....3....1....1....1....0....5....2....6....0....0....0
..4....3....8....2....1....1....3....4....6....5....1....5....4....4....8....8
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..6839

Crossrefs

Row 1 is A004275(n+2).

Row 2 is A067728.

Formula

Empirical for row n:

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

n=2: a(n) = 2*n^2 + 8*n

n=3: a(n) = 2*a(n-1) +a(n-2) -4*a(n-3) +a(n-4) +2*a(n-5) -a(n-6); also a polynomial of degree 3 plus a quasipolynomial of degree 1 with period 2

n=4: a(n) = (14/3)*n^4 + (56/3)*n^3 + (121/3)*n^2 - (5/3)*n + 2

n=5: [linear recurrence of order 10; also a polynomial of degree 5 plus a quasipolynomial of degree 3 with period 2]

n=6: a(n) = (1987/180)*n^6 + (2033/30)*n^5 + (2785/18)*n^4 + 226*n^3 - (3017/180)*n^2 + (697/30)*n

n=7: [order 14; also a polynomial of degree 7 plus a quasipolynomial of degree 5 with period 2]