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

1,1

Comments

Row 4 of A247533

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)

Example

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

Crossrefs

Sequence in context: A303184 A302325 A303018 * A302822 A303515 A027768

Adjacent sequences: A247533 A247534 A247535 * A247537 A247538 A247539

Keyword

nonn

Author

R. H. Hardin, Sep 18 2014

Status

approved