A249531 Number of length 1+5 0..n arrays with no six consecutive terms having five times any element equal to the sum of the remaining five

62, 606, 3492, 13580, 40950, 104562, 235196, 480912, 911490, 1625210, 2754672, 4474896, 7011302, 10648350, 15739200, 22716332, 32101806, 44520162, 60709580, 81535980, 108006522, 141284426, 182704032, 233787120, 296259530, 372068862

Offset

1,1

Comments

Row 1 of A249530

Links

R. H. Hardin, Table of n, a(n) for n = 1..101

Formula

Empirical: a(n) = 4*a(n-1) -6*a(n-2) +5*a(n-3) -4*a(n-4) +3*a(n-5) -2*a(n-6) +2*a(n-7) -2*a(n-9) +2*a(n-10) -3*a(n-11) +4*a(n-12) -5*a(n-13) +6*a(n-14) -4*a(n-15) +a(n-16)

Also a degree 6 polynomial plus a degree 0 quasipolynomial with period 60, the first 12 being:

Empirical for n mod 60 = 0: a(n) = n^6 + (24/5)*n^5 + (51/4)*n^4 + (49/3)*n^3 + 13*n^2 + 5*n

Empirical for n mod 60 = 1: a(n) = n^6 + (24/5)*n^5 + (51/4)*n^4 + (49/3)*n^3 + 13*n^2 + 5*n + (547/60)

Empirical for n mod 60 = 2: a(n) = n^6 + (24/5)*n^5 + (51/4)*n^4 + (49/3)*n^3 + 13*n^2 + 5*n - (124/15)

Empirical for n mod 60 = 3: a(n) = n^6 + (24/5)*n^5 + (51/4)*n^4 + (49/3)*n^3 + 13*n^2 + 5*n - (183/20)

Empirical for n mod 60 = 4: a(n) = n^6 + (24/5)*n^5 + (51/4)*n^4 + (49/3)*n^3 + 13*n^2 + 5*n + (472/15)

Empirical for n mod 60 = 5: a(n) = n^6 + (24/5)*n^5 + (51/4)*n^4 + (49/3)*n^3 + 13*n^2 + 5*n - (425/12)

Empirical for n mod 60 = 6: a(n) = n^6 + (24/5)*n^5 + (51/4)*n^4 + (49/3)*n^3 + 13*n^2 + 5*n + (156/5)

Empirical for n mod 60 = 7: a(n) = n^6 + (24/5)*n^5 + (51/4)*n^4 + (49/3)*n^3 + 13*n^2 + 5*n - (821/60)

Empirical for n mod 60 = 8: a(n) = n^6 + (24/5)*n^5 + (51/4)*n^4 + (49/3)*n^3 + 13*n^2 + 5*n + (344/15)

Empirical for n mod 60 = 9: a(n) = n^6 + (24/5)*n^5 + (51/4)*n^4 + (49/3)*n^3 + 13*n^2 + 5*n - (879/20)

Empirical for n mod 60 = 10: a(n) = n^6 + (24/5)*n^5 + (51/4)*n^4 + (49/3)*n^3 + 13*n^2 + 5*n + (80/3)

Empirical for n mod 60 = 11: a(n) = n^6 + (24/5)*n^5 + (51/4)*n^4 + (49/3)*n^3 + 13*n^2 + 5*n + (1547/60)

Example

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

Crossrefs

Sequence in context: A362458 A069473 A249530 * A069966 A290285 A286212

Adjacent sequences: A249528 A249529 A249530 * A249532 A249533 A249534

Keyword

nonn

Author

R. H. Hardin, Oct 31 2014

Status

approved