A247928 Number of length 1+4 0..n arrays with some disjoint pairs in every consecutive five terms having the same sum.

32, 203, 824, 2365, 5496, 11167, 20648, 35249, 56960, 87211, 128592, 183253, 254144, 343535, 455336, 592177, 758328, 956899, 1192760, 1469381, 1792352, 2165263, 2594304, 3083785, 3640256, 4268147, 4974968, 5765509, 6647640, 7626631, 8710952

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-3) - 2*a(n-5) + 2*a(n-6) + a(n-8) - 2*a(n-10) + a(n-11).

Empirical for n mod 12 = 0: a(n) = 10*n^4 - 20*n^3 + 75*n^2 - 29*n + 1

Empirical for n mod 12 = 1: a(n) = 10*n^4 - 20*n^3 + 75*n^2 - 14*n - 19

Empirical for n mod 12 = 2: a(n) = 10*n^4 - 20*n^3 + 75*n^2 - 29*n - 39

Empirical for n mod 12 = 3: a(n) = 10*n^4 - 20*n^3 + 75*n^2 - 14*n - 79

Empirical for n mod 12 = 4: a(n) = 10*n^4 - 20*n^3 + 75*n^2 - 29*n + 1

Empirical for n mod 12 = 5: a(n) = 10*n^4 - 20*n^3 + 75*n^2 - 14*n - 59

Empirical for n mod 12 = 6: a(n) = 10*n^4 - 20*n^3 + 75*n^2 - 29*n + 1

Empirical for n mod 12 = 7: a(n) = 10*n^4 - 20*n^3 + 75*n^2 - 14*n - 79

Empirical for n mod 12 = 8: a(n) = 10*n^4 - 20*n^3 + 75*n^2 - 29*n - 39

Empirical for n mod 12 = 9: a(n) = 10*n^4 - 20*n^3 + 75*n^2 - 14*n - 19

Empirical for n mod 12 = 10: a(n) = 10*n^4 - 20*n^3 + 75*n^2 - 29*n + 1

Empirical for n mod 12 = 11: a(n) = 10*n^4 - 20*n^3 + 75*n^2 - 14*n - 119.

Empirical g.f.: x*(32 + 139*x + 418*x^2 + 749*x^3 + 969*x^4 + 1063*x^5 + 1021*x^6 + 691*x^7+ 679*x^8 - 2*x^9 + x^10) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Nov 07 2018

Example

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

Crossrefs

Row 1 of A247927.

Sequence in context: A350740 A232051 A247927 * A184020 A283336 A223023

Adjacent sequences: A247925 A247926 A247927 * A247929 A247930 A247931

Keyword

nonn

Author

R. H. Hardin, Sep 26 2014

Status

approved