A248070 Number of length 2+5 0..n arrays with some disjoint triples in each consecutive six terms having the same sum

32, 513, 3364, 15125, 48316, 131677, 299968, 625269, 1174080, 2085341, 3462212, 5539433, 8458164, 12578465, 18080936, 25484457, 35000808, 47350769, 62767700, 82210901, 105929332, 135165573, 170162104, 212500725, 262397536, 321818557

Offset

1,1

Comments

Row 2 of A248068

Links

R. H. Hardin, Table of n, a(n) for n = 1..55

Formula

Empirical: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) -6*a(n-5) -3*a(n-6) +4*a(n-7) +6*a(n-8) +4*a(n-9) -3*a(n-10) -6*a(n-11) -2*a(n-12) +2*a(n-13) +3*a(n-14) -a(n-16)

Empirical for n mod 12 = 0: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (4450/9)*n^3 - (13225/24)*n^2 + (467/6)*n + 1

Empirical for n mod 12 = 1: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (68545/144)*n^3 - (21725/48)*n^2 - (25423/96)*n + (115843/288)

Empirical for n mod 12 = 2: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (4450/9)*n^3 - (13225/24)*n^2 + (49/2)*n + (2269/9)

Empirical for n mod 12 = 3: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (68545/144)*n^3 - (21725/48)*n^2 - (25423/96)*n + (17067/32)

Empirical for n mod 12 = 4: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (4450/9)*n^3 - (13225/24)*n^2 + (467/6)*n - (631/9)

Empirical for n mod 12 = 5: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (68545/144)*n^3 - (21725/48)*n^2 - (10181/32)*n + (214403/288)

Empirical for n mod 12 = 6: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (4450/9)*n^3 - (13225/24)*n^2 + (467/6)*n - 19

Empirical for n mod 12 = 7: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (68545/144)*n^3 - (21725/48)*n^2 - (25423/96)*n + (133123/288)

Empirical for n mod 12 = 8: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (4450/9)*n^3 - (13225/24)*n^2 + (49/2)*n + (2449/9)

Empirical for n mod 12 = 9: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (68545/144)*n^3 - (21725/48)*n^2 - (25423/96)*n + (15147/32)

Empirical for n mod 12 = 10: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (4450/9)*n^3 - (13225/24)*n^2 + (467/6)*n - (811/9)

Empirical for n mod 12 = 11: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (68545/144)*n^3 - (21725/48)*n^2 - (10181/32)*n + (231683/288)

Example

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

Crossrefs

Sequence in context: A035711 A035477 A109384 * A366551 A146124 A125489

Adjacent sequences: A248067 A248068 A248069 * A248071 A248072 A248073

Keyword

nonn

Author

R. H. Hardin, Sep 30 2014

Status

approved