A248539 Number of length 2+3 0..n arrays with every four consecutive terms having the sum of some three elements equal to three times the fourth

2, 15, 52, 113, 246, 427, 704, 1113, 1654, 2279, 3072, 4045, 5210, 6555, 8116, 9953, 12054, 14383, 16976, 19929, 23194, 26735, 30636, 34993, 39686, 44751, 50212, 56201, 62646, 69451, 76712, 84609, 93010, 101879, 111252, 121321, 131942, 143103, 154840

Offset

1,1

Comments

Row 2 of A248537

Links

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

Formula

Empirical: a(n) = a(n-1) -a(n-2) +a(n-4) +a(n-7) +a(n-8) -a(n-9) +a(n-10) -a(n-12) -a(n-13) -a(n-15) -a(n-16) +a(n-18) -a(n-19) +a(n-20) +a(n-21) +a(n-24) -a(n-26) +a(n-27) -a(n-28)

Empirical also a cubic polynomial plus a linear quasipolynomial with period 360, the first 12 being:

Empirical for n mod 360 = 0: a(n) = (11/4)*n^3 - (113/20)*n^2 + (97/10)*n + 1

Empirical for n mod 360 = 1: a(n) = (11/4)*n^3 - (113/20)*n^2 + (209/20)*n - (111/20)

Empirical for n mod 360 = 2: a(n) = (11/4)*n^3 - (113/20)*n^2 + (97/10)*n - (19/5)

Empirical for n mod 360 = 3: a(n) = (11/4)*n^3 - (113/20)*n^2 + (149/20)*n + (25/4)

Empirical for n mod 360 = 4: a(n) = (11/4)*n^3 - (113/20)*n^2 + (97/10)*n - (57/5)

Empirical for n mod 360 = 5: a(n) = (11/4)*n^3 - (113/20)*n^2 + (209/20)*n - (35/4)

Empirical for n mod 360 = 6: a(n) = (11/4)*n^3 - (113/20)*n^2 + (97/10)*n - (109/5)

Empirical for n mod 360 = 7: a(n) = (11/4)*n^3 - (113/20)*n^2 + (149/20)*n - (291/20)

Empirical for n mod 360 = 8: a(n) = (11/4)*n^3 - (113/20)*n^2 + (97/10)*n - 11

Empirical for n mod 360 = 9: a(n) = (11/4)*n^3 - (113/20)*n^2 + (209/20)*n + (257/20)

Empirical for n mod 360 = 10: a(n) = (11/4)*n^3 - (113/20)*n^2 + (97/10)*n - 3

Empirical for n mod 360 = 11: a(n) = (11/4)*n^3 - (113/20)*n^2 + (149/20)*n + (269/20)

Example

Some solutions for n=6
..0....3....5....2....2....2....5....0....0....6....6....1....2....4....6....0
..1....5....6....3....2....2....4....6....3....1....0....5....3....5....2....6
..2....4....5....1....4....3....3....6....2....4....0....6....6....5....4....3
..1....0....4....6....0....5....4....4....3....5....2....4....1....6....4....3
..4....3....1....2....2....2....5....0....0....6....6....5....2....4....6....0

Crossrefs

Sequence in context: A066562 A073877 A248538 * A248540 A007972 A248541

Adjacent sequences: A248536 A248537 A248538 * A248540 A248541 A248542

Keyword

nonn

Author

R. H. Hardin, Oct 08 2014

Status

approved