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A202127 Number of -n..n arrays of 6 elements with first, second and third differences also in -n..n 1

%I #5 Mar 31 2012 12:36:46

%S 35,663,4763,21093,69573,188505,443169,936715,1822729,3318565,5722319,

%T 9430801,14956593,22952527,34234227,49800691,70867027,98891365,

%U 135597851,183019459,243528297,319860401,415169845,533062403,677620099,853469649

%N Number of -n..n arrays of 6 elements with first, second and third differences also in -n..n

%C Row 6 of A202124

%H R. H. Hardin, <a href="/A202127/b202127.txt">Table of n, a(n) for n = 1..194</a>

%F Empirical: a(n) = -a(n-1) -3*a(n-2) -a(n-3) -3*a(n-4) +2*a(n-5) +7*a(n-7) +4*a(n-8) +11*a(n-9) +6*a(n-10) +10*a(n-11) +2*a(n-12) +2*a(n-13) -7*a(n-14) -9*a(n-15) -16*a(n-16) -17*a(n-17) -19*a(n-18) -17*a(n-19) -12*a(n-20) -7*a(n-21) +3*a(n-22) +7*a(n-23) +18*a(n-24) +18*a(n-25) +27*a(n-26) +21*a(n-27) +26*a(n-28) +14*a(n-29) +15*a(n-30) -15*a(n-33) -14*a(n-34) -26*a(n-35) -21*a(n-36) -27*a(n-37) -18*a(n-38) -18*a(n-39) -7*a(n-40) -3*a(n-41) +7*a(n-42) +12*a(n-43) +17*a(n-44) +19*a(n-45) +17*a(n-46) +16*a(n-47) +9*a(n-48) +7*a(n-49) -2*a(n-50) -2*a(n-51) -10*a(n-52) -6*a(n-53) -11*a(n-54) -4*a(n-55) -7*a(n-56) -2*a(n-58) +3*a(n-59) +a(n-60) +3*a(n-61) +a(n-62) +a(n-63)

%e Some solutions for n=5

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Dec 11 2011

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