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

1,1

Comments

Row 2 of A249290

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)

Example

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

Crossrefs

Sequence in context: A200874 A027280 A006354 * A279744 A214353 A283567

Adjacent sequences: A249289 A249290 A249291 * A249293 A249294 A249295

Keyword

nonn

Author

R. H. Hardin, Oct 24 2014

Status

approved