A248491 Number of length 2+5 0..n arrays with some three disjoint pairs in each consecutive six terms having the same sum.

22, 183, 844, 2605, 6306, 13147, 24208, 40449, 64030, 96391, 139212, 195013, 265714, 353595, 462136, 593137, 749598, 935839, 1154140, 1407621, 1701562, 2038603, 2422584, 2859145, 3351406, 3903807, 4522948, 5211829, 5975610, 6821731, 7753672

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-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-8) - 2*a(n-9) + a(n-10) - 2*a(n-11) + a(n-12).

Empirical for n mod 12 = 0: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n + 1

Empirical for n mod 12 = 1: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n - (17/18)

Empirical for n mod 12 = 2: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + (193/3)*n + (1009/9)

Empirical for n mod 12 = 3: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n + (167/2)

Empirical for n mod 12 = 4: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n + (329/9)

Empirical for n mod 12 = 5: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + (193/3)*n + (1343/18)

Empirical for n mod 12 = 6: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n + 1

Empirical for n mod 12 = 7: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n + (2143/18)

Empirical for n mod 12 = 8: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + (193/3)*n + (1009/9)

Empirical for n mod 12 = 9: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n - (73/2)

Empirical for n mod 12 = 10: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n + (329/9)

Empirical for n mod 12 = 11: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + (193/3)*n + (3503/18).

Empirical g.f.: x*(22 + 139*x + 500*x^2 + 1056*x^3 + 1640*x^4 + 2001*x^5 + 1542*x^6 + 383*x^7 - 102*x^8 - 700*x^9 - 2*x^10 + x^11) / ((1 - x)^5*(1 + x)*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, Nov 08 2018

Example

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

Crossrefs

Row 2 of A248489.

Sequence in context: A372996 A248490 A191012 * A248492 A248493 A248494

Adjacent sequences: A248488 A248489 A248490 * A248492 A248493 A248494

Keyword

nonn

Author

R. H. Hardin, Oct 07 2014

Status

approved