A200837 Number of 0..7 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.
400, 2444, 15128, 93472, 577660, 3570086, 22063924, 136360286, 842739040, 5208328180, 32188710564, 198933910242, 1229459024390, 7598350081290, 46959616234372, 290221631449614, 1793638920327662, 11085116434803236
Offset: 1
Keywords
Examples
Some solutions for n=3 ..7....3....6....6....2....3....0....3....7....0....2....1....1....0....3....0 ..2....3....5....0....3....5....4....2....1....5....0....0....7....0....2....3 ..7....6....6....4....2....5....2....7....4....4....4....5....3....4....2....3 ..4....1....6....0....5....5....5....1....2....7....0....0....4....2....6....0 ..7....5....5....5....2....3....0....1....4....6....0....4....4....4....5....0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = 8*a(n-1) -12*a(n-2) +6*a(n-3) -10*a(n-4) +12*a(n-5) -11*a(n-6) +11*a(n-7) -6*a(n-8) +3*a(n-9) -a(n-10).
Empirical g.f.: 2*x*(200 - 378*x + 188*x^2 - 312*x^3 + 378*x^4 - 329*x^5 + 338*x^6 - 183*x^7 + 92*x^8 - 32*x^9) / (1 - 8*x + 12*x^2 - 6*x^3 + 10*x^4 - 12*x^5 + 11*x^6 - 11*x^7 + 6*x^8 - 3*x^9 + x^10). - Colin Barker, Oct 16 2017
Comments