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Number of 0..n arrays x(0..5) of 6 elements with zero 3rd differences.
1

%I #8 May 20 2018 13:15:43

%S 2,3,6,9,14,25,36,47,64,87,110,143,176,209,258,311,364,431,498,575,

%T 666,761,856,969,1092,1219,1364,1513,1662,1847,2032,2221,2432,2647,

%U 2876,3135,3394,3657,3946,4257,4568,4913,5258,5607,6004,6409,6814,7257,7700,8169

%N Number of 0..n arrays x(0..5) of 6 elements with zero 3rd differences.

%C Row 4 of A200272.

%H R. H. Hardin, <a href="/A200273/b200273.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = a(n-3) +a(n-5) +a(n-6) -a(n-8) -a(n-9) +a(n-10) -a(n-11) -a(n-13) +a(n-14) -a(n-15) -a(n-16) +a(n-18) +a(n-19) +a(n-21) -a(n-24).

%F Empirical g.f.: x*(2 + 3*x + 6*x^2 + 7*x^3 + 11*x^4 + 17*x^5 + 22*x^6 + 24*x^7 + 26*x^8 + 33*x^9 + 31*x^10 + 32*x^11 + 26*x^12 + 26*x^13 + 21*x^14 + 15*x^15 + 10*x^16 + 8*x^17 + 6*x^18 + 3*x^19 + 3*x^20 + x^21 - x^23) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x + x^2)^2*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)^2). - _Colin Barker_, May 20 2018

%e Some solutions for n=6:

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

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

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

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

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

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

%Y Cf. A200272.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 15 2011