A247536 Number of length 4+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.

8, 81, 364, 1007, 2164, 3997, 6584, 10219, 14852, 20847, 28108, 37095, 47564, 60087, 74428, 91101, 109760, 131243, 154956, 181677, 211024, 243709, 279136, 318445, 360676, 406933, 456648, 510683, 568172, 630613, 696744, 767859, 843244, 923955

Offset: 1

Author

R. H. Hardin, Sep 18 2014

Keywords

• nonn

Comments

Row 4 of A247533

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..349

Formula

Empirical: a(n) = -a(n-1) -a(n-2) +a(n-4) +2*a(n-5) +3*a(n-6) +3*a(n-7) +2*a(n-8) -2*a(n-10) -4*a(n-11) -4*a(n-12) -4*a(n-13) -2*a(n-14) +2*a(n-16) +3*a(n-17) +3*a(n-18) +2*a(n-19) +a(n-20) -a(n-22) -a(n-23) -a(n-24)

Also as a cubic plus a linear quasipolynomial with period 420, first 12 listed:

Empirical for n mod 420 = 0: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (4243/210)*n + 1

Empirical for n mod 420 = 1: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (2003/210)*n + (622/45)

Empirical for n mod 420 = 2: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (3263/210)*n + (3998/315)

Empirical for n mod 420 = 3: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (2003/210)*n + (148/5)

Empirical for n mod 420 = 4: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (4243/210)*n - (3821/315)

Empirical for n mod 420 = 5: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (341/70)*n + (3580/63)

Empirical for n mod 420 = 6: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (4243/210)*n - (404/35)

Empirical for n mod 420 = 7: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (2003/210)*n + (784/45)

Empirical for n mod 420 = 8: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (3263/210)*n + (1187/45)

Empirical for n mod 420 = 9: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (2003/210)*n + (886/35)

Empirical for n mod 420 = 10: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (4243/210)*n - (184/9)

Empirical for n mod 420 = 11: a(n) = (15541/630)*n^3 - (1401/35)*n^2 + (341/70)*n + (20294/315)