A249498 Number of length 1+5 0..n arrays with every six consecutive terms having five times some element equal to the sum of the remaining five.

2, 123, 604, 2045, 5706, 13087, 26948, 50529, 88510, 146351, 231312, 351913, 518234, 742275, 1038016, 1421237, 1910418, 2525719, 3290420, 4230141, 5373382, 6751463, 8398944, 10353505, 12656246, 15351627, 18488128, 22117469, 26295930, 31083331

Offset

1,1

Comments

Row 1 of A249497

Links

R. H. Hardin, Table of n, a(n) for n = 1..111

Formula

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +2*a(n-3) -2*a(n-4) +a(n-5) -a(n-6) +a(n-7) +a(n-8) -a(n-9) +a(n-10) -2*a(n-11) +2*a(n-12) -3*a(n-13) +3*a(n-14) -a(n-15)

Empirical for n mod 60 = 0: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n + 1

Empirical for n mod 60 = 1: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n - (487/60)

Empirical for n mod 60 = 2: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n + (139/15)

Empirical for n mod 60 = 3: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n + (203/20)

Empirical for n mod 60 = 4: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n - (457/15)

Empirical for n mod 60 = 5: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n + (437/12)

Empirical for n mod 60 = 6: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n - (151/5)

Empirical for n mod 60 = 7: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n + (881/60)

Empirical for n mod 60 = 8: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n - (329/15)

Empirical for n mod 60 = 9: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n + (899/20)

Empirical for n mod 60 = 10: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n - (77/3)

Empirical for n mod 60 = 11: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n - (1487/60)

Example

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

Crossrefs

Sequence in context: A013471 A370967 A249497 * A249499 A249500 A249501

Adjacent sequences: A249495 A249496 A249497 * A249499 A249500 A249501

Keyword

nonn

Author

R. H. Hardin, Oct 30 2014

Status

approved