A248492 Number of length 3+5 0..n arrays with some three disjoint pairs in each consecutive six terms having the same sum

22, 183, 988, 3301, 8370, 17923, 33520, 55665, 87310, 129991, 185340, 256861, 346258, 456195, 590920, 751873, 942030, 1167247, 1428940, 1730397, 2078794, 2475475, 2924280, 3433177, 4003774, 4640463, 5351908, 6140413, 7010538, 7972267

Offset

1,1

Comments

Row 3 of A248489

Links

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

Formula

Empirical: a(n) = -a(n-2) +a(n-3) +2*a(n-5) +a(n-6) +2*a(n-7) +a(n-8) -a(n-10) -3*a(n-11) -2*a(n-12) -4*a(n-13) -a(n-14) -2*a(n-15) +2*a(n-16) +a(n-17) +4*a(n-18) +2*a(n-19) +3*a(n-20) +a(n-21) -a(n-23) -2*a(n-24) -a(n-25) -2*a(n-26) -a(n-28) +a(n-29) +a(n-31)

Also a quartic polynomial plus a linear quasipolynomial with period 840, the first 12 being:

Empirical for n mod 840 = 0: a(n) = (15/2)*n^4 + (701/9)*n^3 - (23846/105)*n^2 - (1769/35)*n + 1

Empirical for n mod 840 = 1: a(n) = (15/2)*n^4 + (701/9)*n^3 - (23846/105)*n^2 - (1664/35)*n + (133093/630)

Empirical for n mod 840 = 2: a(n) = (15/2)*n^4 + (701/9)*n^3 - (23846/105)*n^2 - (10907/105)*n + (175159/315)

Empirical for n mod 840 = 3: a(n) = (15/2)*n^4 + (701/9)*n^3 - (23846/105)*n^2 - (2084/35)*n + (7001/14)

Empirical for n mod 840 = 4: a(n) = (15/2)*n^4 + (701/9)*n^3 - (23846/105)*n^2 - (1769/35)*n + (73067/315)

Empirical for n mod 840 = 5: a(n) = (15/2)*n^4 + (701/9)*n^3 - (23846/105)*n^2 - (10592/105)*n + (2311/18)

Empirical for n mod 840 = 6: a(n) = (15/2)*n^4 + (701/9)*n^3 - (23846/105)*n^2 - (1769/35)*n - (4969/35)

Empirical for n mod 840 = 7: a(n) = (15/2)*n^4 + (701/9)*n^3 - (23846/105)*n^2 - (2084/35)*n + (30739/90)

Empirical for n mod 840 = 8: a(n) = (15/2)*n^4 + (701/9)*n^3 - (23846/105)*n^2 - (10907/105)*n + (27191/63)

Empirical for n mod 840 = 9: a(n) = (15/2)*n^4 + (701/9)*n^3 - (23846/105)*n^2 - (1664/35)*n + (10141/70)

Empirical for n mod 840 = 10: a(n) = (15/2)*n^4 + (701/9)*n^3 - (23846/105)*n^2 - (1769/35)*n + (20035/63)

Empirical for n mod 840 = 11: a(n) = (15/2)*n^4 + (701/9)*n^3 - (23846/105)*n^2 - (11852/105)*n + (367733/630)

Example

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

Crossrefs

Sequence in context: A248490 A191012 A248491 * A248493 A248494 A248495

Adjacent sequences: A248489 A248490 A248491 * A248493 A248494 A248495

Keyword

nonn

Author

R. H. Hardin, Oct 07 2014

Status

approved