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A247536
Number of length 4+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 18 2014
STATUS
approved