A249292 Number of length 2+3 0..n arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

26, 168, 660, 2228, 5646, 12600, 25280, 46608, 80334, 131672, 206112, 311352, 455954, 649920, 904884, 1235024, 1654734, 2181960, 2836016, 3638460, 4613010, 5786924, 7188012, 8848968, 10803998, 13090368, 15748356, 18822884, 22359246

Offset: 1

Author

R. H. Hardin, Oct 24 2014

Keywords

• nonn

Comments

Row 2 of A249290

Examples

			Some solutions for n=10
..4....0....9....7....5....3....9....2....1....3....3....1....1....5....1....4
..7....3....7....5....3....2....5....5....5....2....7....7...10....6....6...10
..4....7....2...10...10....8....6....8....3....1....5...10....1....6....9....3
..3....1....1....8...10....2....5....9....6...10....3....5....9....6...10....6
..7....0....0....2....6....8....9....3....7....9....4....7....7....7....5....0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 2*a(n-1) -2*a(n-2) +2*a(n-3) -a(n-4) +a(n-5) -a(n-6) +a(n-8) -2*a(n-9) +a(n-10) -a(n-11) +a(n-12) -2*a(n-13) +2*a(n-14) +2*a(n-18) -2*a(n-19) +a(n-20) -a(n-21) +a(n-22) -2*a(n-23) +a(n-24) -a(n-26) +a(n-27) -a(n-28) +2*a(n-29) -2*a(n-30) +2*a(n-31) -a(n-32)

Also a polynomial of degree 5 plus a linear quasipolynomial with period 360, the first 12 being:

Empirical for n mod 360 = 0: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (107/10)*n

Empirical for n mod 360 = 1: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (967/60)*n - (113/60)

Empirical for n mod 360 = 2: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (481/30)*n + (8/15)

Empirical for n mod 360 = 3: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (49/20)*n - (3/4)

Empirical for n mod 360 = 4: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (641/30)*n - (26/15)

Empirical for n mod 360 = 5: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (647/60)*n - (125/12)

Empirical for n mod 360 = 6: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (107/10)*n - (114/5)

Empirical for n mod 360 = 7: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (787/60)*n - (653/60)

Empirical for n mod 360 = 8: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (481/30)*n - (20/3)

Empirical for n mod 360 = 9: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (109/20)*n + (117/20)

Empirical for n mod 360 = 10: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (641/30)*n + (20/3)

Empirical for n mod 360 = 11: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (467/60)*n + (707/60)