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A250169
Number of length 4+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 13 2014
STATUS
approved