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%I #10 Feb 12 2018 21:04:52
%S 2,3,4,5,6,13,20,27,36,49,62,81,100,119,146,177,208,247,286,329,380,
%T 435,490,555,624,697,780,867,954,1059,1164,1273,1394,1519,1648,1797,
%U 1946,2099,2264,2441,2618,2817,3016,3219,3444,3677,3910,4165,4420,4687,4974
%N Number of 0..n arrays x(0..6) of 7 elements with zero 3rd differences
%C Row 4 of A200329
%H R. H. Hardin, <a href="/A200330/b200330.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = a(n-1) -a(n-3) +a(n-4) +a(n-9) -a(n-11) +a(n-12) -a(n-14) +a(n-15) -a(n-16) +a(n-18) -2*a(n-19) +a(n-20) -a(n-22) +a(n-23) -a(n-24) +a(n-26) -a(n-27) +a(n-29) +a(n-34) -a(n-35) +a(n-37) -a(n-38).
%F Empirical: G.f.: -x*(-2 -x -x^2 -35*x^20 -27*x^21 -29*x^22 -24*x^23 -18*x^24 -19*x^25 -2*x^30- 2*x^31 -2*x^32 -2*x^33 -x^35 -x^36 +x^37 -14*x^26 -8*x^27 -9*x^28 -8*x^29 -3*x^3 -2*x^4 -8*x^5 -8*x^6 -8*x^7 -16*x^8 -18*x^9 -17*x^10 -26*x^11 -28*x^12 -27*x^13 -36*x^14 -32*x^15 -33*x^16 -41*x^17 -31*x^18 -34*x^19) / ( (x^2-x+1) *(x^4-x^3+x^2-x+1) *(x^6+x^3+1) *(x^8-x^7+x^5-x^4+x^3-x+1)* (1+x)^2 *(1+x+x^2)^2 *(x^4+x^3+x^2+x+1)^2 *(x-1)^4 ). - _R. J. Mathar_, Mar 07 2015
%e All solutions for n=6
%e ..6....4....0....6....1....3....3....5....0....2....6....0....3
%e ..6....4....0....3....1....5....3....5....3....2....5....1....1
%e ..6....4....0....1....1....6....3....5....5....2....4....2....0
%e ..6....4....0....0....1....6....3....5....6....2....3....3....0
%e ..6....4....0....0....1....5....3....5....6....2....2....4....1
%e ..6....4....0....1....1....3....3....5....5....2....1....5....3
%e ..6....4....0....3....1....0....3....5....3....2....0....6....6
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 16 2011
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