A248538 Number of length 1+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, 101, 198, 331, 512, 753, 1066, 1439, 1908, 2461, 3110, 3867, 4744, 5729, 6858, 8119, 9524, 11085, 12814, 14699, 16776, 19033, 21482, 24135, 27004, 30077, 33390, 36931, 40712, 44745, 49042, 53591, 58428, 63541, 68942, 74643, 80656, 86969

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-3) - a(n-4) + 2*a(n-6) - a(n-7).

Empirical for n mod 6 = 0: a(n) = (4/3)*n^3 + n^2 + n + 1.

Empirical for n mod 6 = 1: a(n) = (4/3)*n^3 + n^2 + n - (4/3).

Empirical for n mod 6 = 2: a(n) = (4/3)*n^3 + n^2 + n - (5/3).

Empirical for n mod 6 = 3: a(n) = (4/3)*n^3 + n^2 + n + 4.

Empirical for n mod 6 = 4: a(n) = (4/3)*n^3 + n^2 + n - (13/3).

Empirical for n mod 6 = 5: a(n) = (4/3)*n^3 + n^2 + n + (4/3).

Empirical g.f.: x*(2 + 11*x + 22*x^2 - x^3 + 13*x^4 + 2*x^5 - x^6) / ((1 - x)^4*(1 + x)*(1 + x + x^2)). - Colin Barker, Nov 08 2018

Example

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

Crossrefs

Row 1 of A248537.

Sequence in context: A154565 A066562 A073877 * A248539 A248540 A007972

Adjacent sequences: A248535 A248536 A248537 * A248539 A248540 A248541

Keyword

nonn

Author

R. H. Hardin, Oct 08 2014

Status

approved