A251937 - OEIS

%I #8 Dec 01 2018 06:55:24

%S 18,115,431,1191,2695,5340,9615,16098,25474,38538,56176,79403,109350,

%T 147253,194487,252561,323091,407854,508767,627868,767366,929628,

%U 1117144,1332597,1578834,1858839,2175799,2533083,2934199,3382880,3883047,4438774

%N Number of length 3+2 0..n arrays with the sum of the maximum minus the median of adjacent triples multiplied by some arrangement of +-1 equal to zero.

%H R. H. Hardin, <a href="/A251937/b251937.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 3*a(n-4) + 3*a(n-5) + 3*a(n-6) - 3*a(n-7) - 2*a(n-9) + 3*a(n-10) - a(n-11).

%F Empirical for n mod 6 = 0: a(n) = (1/30)*n^5 + (653/216)*n^4 + (239/54)*n^3 + 5*n^2 + (43/10)*n + 1

%F Empirical for n mod 6 = 1: a(n) = (1/30)*n^5 + (653/216)*n^4 + (239/54)*n^3 + 5*n^2 + (1241/270)*n + (199/216)

%F Empirical for n mod 6 = 2: a(n) = (1/30)*n^5 + (653/216)*n^4 + (239/54)*n^3 + 5*n^2 + (1201/270)*n + (34/27)

%F Empirical for n mod 6 = 3: a(n) = (1/30)*n^5 + (653/216)*n^4 + (239/54)*n^3 + 5*n^2 + (43/10)*n + (5/8)

%F Empirical for n mod 6 = 4: a(n) = (1/30)*n^5 + (653/216)*n^4 + (239/54)*n^3 + 5*n^2 + (1241/270)*n + (35/27)

%F Empirical for n mod 6 = 5: a(n) = (1/30)*n^5 + (653/216)*n^4 + (239/54)*n^3 + 5*n^2 + (1201/270)*n + (191/216).

%F Empirical g.f.: x*(18 + 61*x + 122*x^2 + 128*x^3 + 38*x^4 - 72*x^5 - 121*x^6 - 78*x^7 - 26*x^8 + 3*x^9 - x^10) / ((1 - x)^6*(1 + x)*(1 + x + x^2)^2). - _Colin Barker_, Dec 01 2018

%e Some solutions for n=6:

%e ..2....1....2....5....6....5....1....1....4....5....3....0....4....3....2....3

%e ..4....0....1....4....2....5....2....6....3....2....5....0....4....1....0....6

%e ..6....3....4....2....5....1....0....2....6....2....3....1....1....5....1....2

%e ..0....4....3....3....3....3....1....6....5....0....0....3....2....4....3....4

%e ..6....1....3....3....4....0....3....1....3....5....3....4....4....0....2....5

%Y Row 3 of A251935.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 11 2014