A247929 Number of length 2+4 0..n arrays with some disjoint pairs in every consecutive five terms having the same sum

64, 529, 2760, 9569, 25512, 57769, 117256, 216937, 376656, 613721, 956736, 1432465, 2078080, 2925313, 4025112, 5420273, 7170312, 9325369, 11960584, 15142537, 18952080, 23466953, 28787520, 35002753, 42229648, 50570737, 60151800, 71100353

Offset

1,1

Comments

Row 2 of A247927

Links

R. H. Hardin, Table of n, a(n) for n = 1..152

Formula

Empirical: a(n) = a(n-2) +a(n-3) +a(n-4) -a(n-7) -2*a(n-8) -2*a(n-9) -a(n-10) +2*a(n-12) +2*a(n-13) +2*a(n-14) +2*a(n-15) -a(n-17) -2*a(n-18) -2*a(n-19) -a(n-20) +a(n-23) +a(n-24) +a(n-25) -a(n-27)

Also a polynomial of degree 5 plus a linear quasipolynomial with period 420; the first 12 are :

Empirical for n mod 420 = 0: a(n) = 2*n^5 + 75*n^4 - (1460/3)*n^3 + (58568/35)*n^2 - (60384/35)*n + 1

Empirical for n mod 420 = 1: a(n) = 2*n^5 + 75*n^4 - (1460/3)*n^3 + (58358/35)*n^2 - (50934/35)*n + (27463/105)

Empirical for n mod 420 = 2: a(n) = 2*n^5 + 75*n^4 - (1460/3)*n^3 + (58568/35)*n^2 - (57024/35)*n - (29047/105)

Empirical for n mod 420 = 3: a(n) = 2*n^5 + 75*n^4 - (1460/3)*n^3 + (58358/35)*n^2 - (50934/35)*n - (9111/7)

Empirical for n mod 420 = 4: a(n) = 2*n^5 + 75*n^4 - (1460/3)*n^3 + (58568/35)*n^2 - (60384/35)*n - (42551/105)

Empirical for n mod 420 = 5: a(n) = 2*n^5 + 75*n^4 - (1460/3)*n^3 + (58358/35)*n^2 - (47574/35)*n - (5003/3)

Empirical for n mod 420 = 6: a(n) = 2*n^5 + 75*n^4 - (1460/3)*n^3 + (58568/35)*n^2 - (60384/35)*n + (8651/35)

Empirical for n mod 420 = 7: a(n) = 2*n^5 + 75*n^4 - (1460/3)*n^3 + (58358/35)*n^2 - (50934/35)*n - (15311/15)

Empirical for n mod 420 = 8: a(n) = 2*n^5 + 75*n^4 - (1460/3)*n^3 + (58568/35)*n^2 - (57024/35)*n - (14435/21)

Empirical for n mod 420 = 9: a(n) = 2*n^5 + 75*n^4 - (1460/3)*n^3 + (58358/35)*n^2 - (50934/35)*n - (24387/35)

Empirical for n mod 420 = 10: a(n) = 2*n^5 + 75*n^4 - (1460/3)*n^3 + (58568/35)*n^2 - (60384/35)*n + (6365/21)

Empirical for n mod 420 = 11: a(n) = 2*n^5 + 75*n^4 - (1460/3)*n^3 + (58358/35)*n^2 - (47574/35)*n - (261217/105)

Example

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

Crossrefs

Sequence in context: A115740 A100415 A200841 * A070054 A265636 A209787

Adjacent sequences: A247926 A247927 A247928 * A247930 A247931 A247932

Keyword

nonn

Author

R. H. Hardin, Sep 26 2014

Status

approved