A200185 Number of -n..n arrays x(0..6) of 7 elements with zero sum and no two consecutive declines, no adjacent equal elements, and no element more than one greater than the previous (random base sawtooth pattern).
10, 29, 78, 100, 186, 246, 380, 464, 686, 798, 1096, 1276, 1658, 1878, 2408, 2668, 3306, 3672, 4432, 4852, 5814, 6288, 7398, 8010, 9278, 9960, 11486, 12236, 13944, 14870, 16774, 17780, 19998, 21088, 23528, 24826, 27494, 28890, 31930, 33424, 36720, 38456
Offset: 1
Keywords
Examples
Some solutions for n=6: ..0....3....1....3....6....2....1....2....4....3...-1....3....1....4....4....3 ..1....4....2....2...-1....3...-1....3....0....4....0....0...-2....5....5....2 ..2....3....0....3....0....4....0...-1....1....5...-1....1...-1...-2....1....3 ..3....4....1...-3....1....5....1....0....2...-4....0...-2....0...-1....2...-2 .-2...-5...-1...-2...-1...-5....2...-1...-2...-3....1...-1....1...-3...-5...-1 .-1...-4....0...-1....0...-4...-2....0...-1...-2....0....0....2...-2...-4....0 .-3...-5...-3...-2...-5...-5...-1...-3...-4...-3....1...-1...-1...-1...-3...-5
Links
- R. H. Hardin, Table of n, a(n) for n = 1..200
Crossrefs
Cf. A200181.
Formula
Empirical: a(n) = -a(n-1) +a(n-3) +2*a(n-4) +2*a(n-5) +2*a(n-6) -2*a(n-8) -3*a(n-9) -3*a(n-10) -2*a(n-11) +2*a(n-13) +2*a(n-14) +2*a(n-15) +a(n-16) -a(n-18) -a(n-19) for n>21.
Empirical g.f.: x*(10 + 39*x + 107*x^2 + 168*x^3 + 237*x^4 + 276*x^5 + 292*x^6 + 244*x^7 + 196*x^8 + 128*x^9 + 79*x^10 + 47*x^11 + 40*x^12 + 30*x^13 + 28*x^14 + 22*x^15 + 8*x^16 - 5*x^17 - 12*x^18 - 9*x^19 - x^20) / ((1 - x)^4*(1 + x)^3*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, May 20 2018
Comments