A228744 Number of arrays of the median of three adjacent elements of some length 9 0..n array.
88, 1071, 6130, 23627, 71278, 181885, 410828, 845517, 1617004, 2913955, 4999182, 8228935, 13075154, 20150881, 30239032, 44324729, 63631392, 89660791, 124237258, 169556259, 228237526, 303382949, 398639428, 518266885, 667211636, 851185323
Offset: 1
Keywords
Examples
Some solutions for n=4: 2 4 0 4 3 2 0 4 1 2 3 1 4 2 1 1 3 1 1 3 0 3 1 2 1 2 2 2 4 2 1 2 2 4 4 2 1 0 1 4 4 3 2 4 0 3 0 3 2 0 2 1 0 0 0 4 3 3 0 4 4 4 4 3 2 2 4 2 0 0 0 4 4 4 2 3 2 4 4 4 0 1 4 2 0 2 1 4 3 4 0 2 4 0 4 2 1 1 4 2 2 4 4 1 0 2 1 2 2 0 4 4
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A228740.
Formula
Empirical: a(n) = (5/126)*n^7 + (4/3)*n^6 + (829/90)*n^5 + (93/4)*n^4 + (509/18)*n^3 + (221/12)*n^2 + (453/70)*n + 1.
Conjectures from Colin Barker, Mar 16 2018: (Start)
G.f.: x*(88 + 367*x + 26*x^2 - 353*x^3 + 86*x^4 - 21*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)
Comments