A248534 Number of length n+3 0..5 arrays with every four consecutive terms having the sum of some three elements equal to three times the fourth.

198, 246, 306, 378, 462, 594, 762, 972, 1230, 1620, 2118, 2748, 3534, 4710, 6222, 8148, 10566, 14160, 18810, 24762, 32262, 43356, 57774, 76290, 99678, 134160, 179106, 236952, 310134, 417798, 558402, 739614, 969102, 1306254, 1747098, 2315772

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 6*a(n-4) - 6*a(n-5) - 11*a(n-8) + 11*a(n-9) + 7*a(n-12) - 7*a(n-13) - 2*a(n-16) + 2*a(n-17).

Empirical g.f.: 6*x*(33 + 8*x + 10*x^2 + 12*x^3 - 184*x^4 - 26*x^5 - 32*x^6 - 37*x^7 + 322*x^8 + 21*x^9 + 25*x^10 + 27*x^11 - 204*x^12 - 8*x^13 - 8*x^14 - 8*x^15 + 58*x^16) / ((1 - x)*(1 - 2*x^4)*(1 - 4*x^4 + 3*x^8 - x^12)). - Colin Barker, Nov 08 2018

Example

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

Crossrefs

Column 5 of A248537.

Sequence in context: A031512 A260193 A025366 * A334403 A238230 A055971

Adjacent sequences: A248531 A248532 A248533 * A248535 A248536 A248537

Keyword

nonn

Author

R. H. Hardin, Oct 08 2014

Status

approved