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A200371 Number of 0..n arrays x(0..8) of 9 elements with zero 3rd differences.

%I A200371 #7 Jul 22 2025 15:47:40
%S A200371 2,3,4,5,6,7,8,11,14,21,28,35,42,49,60,75,90,105,120,139,162,185,208,
%T A200371 233,262,295,328,365,402,447,492,541,590,639,692,757,822,887,952,1027,
%U A200371 1102,1185,1268,1355,1450,1549,1648,1751,1858,1973,2092,2219,2346,2473,2608
%N A200371 Number of 0..n arrays x(0..8) of 9 elements with zero 3rd differences.
%C A200371 Row 4 of A200370
%H A200371 R. H. Hardin, <a href="/A200371/b200371.txt">Table of n, a(n) for n = 1..200</a>
%F A200371 Empirical: a(n) = -a(n-2) -a(n-4) -a(n-6) -a(n-8) +a(n-15) +a(n-16) +a(n-17) +a(n-18) +a(n-19) +a(n-20) +2*a(n-21) +a(n-22) +2*a(n-23) +a(n-24) +a(n-25) +a(n-27) +a(n-28) +a(n-29) +a(n-30) -a(n-31) +a(n-32) -a(n-33) +a(n-34) -a(n-35) -2*a(n-37) -a(n-38) -2*a(n-39) -a(n-40) -a(n-41) -a(n-42) -2*a(n-43) -2*a(n-44) -2*a(n-45) -a(n-46) -a(n-47) -a(n-48) -2*a(n-49) -a(n-50) -2*a(n-51) -a(n-53) +a(n-54) -a(n-55) +a(n-56) -a(n-57) +a(n-58) +a(n-59) +a(n-60) +a(n-61) +a(n-63) +a(n-64) +2*a(n-65) +a(n-66) +2*a(n-67) +a(n-68) +a(n-69) +a(n-70) +a(n-71) +a(n-72) +a(n-73) -a(n-80) -a(n-82) -a(n-84) -a(n-86) -a(n-88)
%e A200371 Some solutions for n=10
%e A200371 ..1....5....8....3....4....6....9...10....0....8...10....2....6....0....0....9
%e A200371 ..1....5....7....3....4....6....9....9....4....8...10....2....3....0....1....8
%e A200371 ..1....5....6....3....4....6....9....8....7....8...10....2....1....0....2....7
%e A200371 ..1....5....5....3....4....6....9....7....9....8...10....2....0....0....3....6
%e A200371 ..1....5....4....3....4....6....9....6...10....8...10....2....0....0....4....5
%e A200371 ..1....5....3....3....4....6....9....5...10....8...10....2....1....0....5....4
%e A200371 ..1....5....2....3....4....6....9....4....9....8...10....2....3....0....6....3
%e A200371 ..1....5....1....3....4....6....9....3....7....8...10....2....6....0....7....2
%e A200371 ..1....5....0....3....4....6....9....2....4....8...10....2...10....0....8....1
%K A200371 nonn
%O A200371 1,1
%A A200371 _R. H. Hardin_ Nov 16 2011