A249360 Number of length 1+6 0..n arrays with every seven consecutive terms having six times some element equal to the sum of the remaining six

2, 395, 2048, 9413, 30848, 84259, 198570, 421913, 823336, 1504241, 2601366, 4297747, 6831608, 10505741, 15697544, 22873679, 32598374, 45551245, 62537376, 84505589, 112561702, 147987947, 192258132, 247057213, 314300264, 396153407

Offset

1,1

Comments

Row 1 of A249359

Links

R. H. Hardin, Table of n, a(n) for n = 1..54

Formula

Empirical: a(n) = 5*a(n-1) -11*a(n-2) +15*a(n-3) -15*a(n-4) +12*a(n-5) -9*a(n-6) +7*a(n-7) -4*a(n-8) +4*a(n-10) -7*a(n-11) +9*a(n-12) -12*a(n-13) +15*a(n-14) -15*a(n-15) +11*a(n-16) -5*a(n-17) +a(n-18)

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

Empirical for n mod 60 = 0: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + 1

Empirical for n mod 60 = 1: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (983/60)

Empirical for n mod 60 = 2: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (467/5)

Empirical for n mod 60 = 3: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (1373/20)

Empirical for n mod 60 = 4: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (967/15)

Empirical for n mod 60 = 5: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (353/4)

Empirical for n mod 60 = 6: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (551/5)

Empirical for n mod 60 = 7: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (7871/60)

Empirical for n mod 60 = 8: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (1013/5)

Empirical for n mod 60 = 9: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (3109/20)

Empirical for n mod 60 = 10: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (143/3)

Empirical for n mod 60 = 11: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (1819/20)

Example

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

Crossrefs

Sequence in context: A249359 A249255 A249171 * A249361 A249362 A249363

Adjacent sequences: A249357 A249358 A249359 * A249361 A249362 A249363

Keyword

nonn

Author

R. H. Hardin, Oct 26 2014

Status

approved