A229017 Number of arrays of median of three adjacent elements of some length 9 0..n array, with no adjacent equal elements in the latter.
2, 193, 2054, 10735, 38768, 111311, 273124, 597477, 1197190, 2238005, 3954490, 6668675, 10811620, 16948115, 25804712, 38301289, 55586346, 79076233, 110498510, 151939639, 205897208, 275336887, 363754316, 475242125, 614562286, 787223997
Offset: 1
Keywords
Examples
Some solutions for n=4: ..2....3....3....0....3....3....4....3....1....3....1....0....1....4....3....4 ..3....4....2....3....4....3....2....3....0....4....1....1....2....3....4....3 ..3....3....2....1....1....1....1....3....2....0....2....2....0....4....1....3 ..2....3....1....3....1....1....1....0....1....4....2....2....4....3....3....0 ..1....3....4....1....1....1....0....3....4....3....1....2....2....2....0....1 ..1....3....2....4....2....4....3....2....1....3....1....1....3....2....3....1 ..2....4....4....1....3....0....3....3....2....1....1....1....3....1....3....3
Links
- R. H. Hardin, Table of n, a(n) for n = 1..158
Crossrefs
Row 7 of A229012.
Formula
Empirical: a(n) = (5/126)*n^7 + (233/180)*n^6 + (1073/180)*n^5 - (85/18)*n^4 - (89/36)*n^3 + (617/180)*n^2 - (177/70)*n + 1.
Conjectures from Colin Barker, Sep 14 2018: (Start)
G.f.: x*(2 + 177*x + 566*x^2 - 405*x^3 - 268*x^4 + 121*x^5 + 8*x^6 - x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)