A248464 Number of length 3+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third

16, 72, 460, 1512, 4272, 9684, 20236, 37868, 67140, 111104, 177024, 269892, 400040, 574140, 806808, 1107132, 1493952, 1978984, 2586340, 3330852, 4242444, 5338788, 6656352, 8217136, 10064140, 12222784, 14744480, 17659176, 21025952, 24879392

Offset

1,1

Comments

Row 3 of A248461

Links

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

Formula

Empirical: a(n) = a(n-1) +a(n-3) -2*a(n-7) +a(n-8) -2*a(n-9) +a(n-10) -a(n-11) +2*a(n-12) +2*a(n-15) -a(n-16) +a(n-17) -2*a(n-18) +a(n-19) -2*a(n-20) +a(n-24) +a(n-26) -a(n-27)

Also a polynomial of degree 5 plus a quadratic quasipolynomial with period 840, the first 12 being:

Empirical for n mod 840 = 0: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (51/5)*n

Empirical for n mod 840 = 1: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (66/5)*n - (33/10)

Empirical for n mod 840 = 2: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (113/15)*n - (152/15)

Empirical for n mod 840 = 3: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (26/5)*n - (1/2)

Empirical for n mod 840 = 4: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (51/5)*n - (12/5)

Empirical for n mod 840 = 5: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (158/15)*n + (1/6)

Empirical for n mod 840 = 6: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (51/5)*n - (24/5)

Empirical for n mod 840 = 7: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (26/5)*n + (67/10)

Empirical for n mod 840 = 8: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (113/15)*n - (4/3)

Empirical for n mod 840 = 9: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (66/5)*n - (9/10)

Empirical for n mod 840 = 10: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (51/5)*n - 8

Empirical for n mod 840 = 11: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (38/15)*n + (41/30)

Example

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

Crossrefs

Sequence in context: A146748 A029872 A056633 * A232572 A363794 A098096

Adjacent sequences: A248461 A248462 A248463 * A248465 A248466 A248467

Keyword

nonn

Author

R. H. Hardin, Oct 06 2014

Status

approved