A250169 Number of length 4+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

16, 119, 436, 1269, 2860, 5831, 10460, 17765, 27984, 42611, 61752, 87477, 119672, 161051, 211212, 273601, 347428, 436963, 540948, 664553, 805976, 971367, 1158288, 1373969, 1615248, 1890503, 2195780, 2540693, 2920396, 3345831, 3811180, 4328789

Offset

1,1

Links

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

Formula

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

Empirical for n mod 12 = 0: a(n) = (197/48)*n^4 + (5/12)*n^3 + (45/4)*n^2 + (8/3)*n + 1

Empirical for n mod 12 = 1: a(n) = (197/48)*n^4 + (5/12)*n^3 + (69/8)*n^2 + (77/12)*n - (57/16)

Empirical for n mod 12 = 2: a(n) = (197/48)*n^4 + (5/12)*n^3 + (45/4)*n^2 + (8/3)*n - (1/3)

Empirical for n mod 12 = 3: a(n) = (197/48)*n^4 + (5/12)*n^3 + (69/8)*n^2 + (77/12)*n - (73/16)

Empirical for n mod 12 = 4: a(n) = (197/48)*n^4 + (5/12)*n^3 + (45/4)*n^2 + (8/3)*n + 1

Empirical for n mod 12 = 5: a(n) = (197/48)*n^4 + (5/12)*n^3 + (69/8)*n^2 + (77/12)*n - (235/48)

Empirical for n mod 12 = 6: a(n) = (197/48)*n^4 + (5/12)*n^3 + (45/4)*n^2 + (8/3)*n + 1

Empirical for n mod 12 = 7: a(n) = (197/48)*n^4 + (5/12)*n^3 + (69/8)*n^2 + (77/12)*n - (73/16)

Empirical for n mod 12 = 8: a(n) = (197/48)*n^4 + (5/12)*n^3 + (45/4)*n^2 + (8/3)*n - (1/3)

Empirical for n mod 12 = 9: a(n) = (197/48)*n^4 + (5/12)*n^3 + (69/8)*n^2 + (77/12)*n - (57/16)

Empirical for n mod 12 = 10: a(n) = (197/48)*n^4 + (5/12)*n^3 + (45/4)*n^2 + (8/3)*n + 1

Empirical for n mod 12 = 11: a(n) = (197/48)*n^4 + (5/12)*n^3 + (69/8)*n^2 + (77/12)*n - (283/48).

Empirical g.f.: x*(16 + 103*x + 285*x^2 + 611*x^3 + 854*x^4 + 1020*x^5 + 852*x^6 + 612*x^7 + 274*x^8 + 101*x^9 - x^10 + x^11) / ((1 - x)^5*(1 + x)^3*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Nov 12 2018

Example

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

Crossrefs

Row 4 of A250167.

Sequence in context: A145216 A200173 A226761 * A210428 A283037 A093740

Adjacent sequences: A250166 A250167 A250168 * A250170 A250171 A250172

Keyword

nonn

Author

R. H. Hardin, Nov 13 2014

Status

approved