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%I #5 Mar 31 2012 12:36:21
%S 1,11,101,491,3141,19301,115761,706591,4292223,26065517,158426129,
%T 962553071,5848496923,35536745667,215924096065,1311980244395,
%U 7971749802937,48437255764809,294310402140129,1788264132674883
%N Number of arrays of -5..5 integers x(1..n) with every x(i) in a subsequence of length 1, 2 or 3 with sum zero
%C Column 5 of A193702
%H R. H. Hardin, <a href="/A193699/b193699.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 7*a(n-1) -10*a(n-2) +12*a(n-3) +40*a(n-4) +244*a(n-5) +3*a(n-6) +1089*a(n-7) +3707*a(n-8) +6208*a(n-9) +11413*a(n-10) +54122*a(n-11) +73396*a(n-12) +158607*a(n-13) +405718*a(n-14) +701801*a(n-15) +1089821*a(n-16) +2395265*a(n-17) +3200288*a(n-18) +4951404*a(n-19) +6944714*a(n-20) +8209743*a(n-21) +6954175*a(n-22) +5206414*a(n-23) -8778901*a(n-24) -18668023*a(n-25) -42468364*a(n-26) -49526242*a(n-27) -51648621*a(n-28) -18663384*a(n-29) +10565942*a(n-30) +78511699*a(n-31) +71823492*a(n-32) +108577171*a(n-33) +19543205*a(n-34) +19288879*a(n-35) -71137204*a(n-36) -42763958*a(n-37) -65244582*a(n-38) -16175672*a(n-39) -11174774*a(n-40) +13423392*a(n-41) +10575176*a(n-42) +12859223*a(n-43) +6625040*a(n-44) +4102636*a(n-45) +1041074*a(n-46) +129924*a(n-47) -376260*a(n-48) -325965*a(n-49) -242219*a(n-50) -129056*a(n-51) -62894*a(n-52) -25836*a(n-53) -9900*a(n-54) -3275*a(n-55) -954*a(n-56) -243*a(n-57) -55*a(n-58) -10*a(n-59) -a(n-60)
%e Some solutions for n=6
%e .-4...-3....2...-4....1...-3...-2...-1....4....1....2....4....4....4....0...-5
%e ..4....3...-2....1....4....3....2....1....1...-5...-2...-4....0...-4....2....5
%e ..1....0....4....3...-5...-5....1....0...-5....4...-5...-2...-4....4...-2...-5
%e .-5....3...-2...-4....3....5....4...-1....5...-1....5....2...-1...-3...-5....4
%e ..2...-5....1....1....2...-5...-5....1....3...-4....0...-4...-2...-2....2...-4
%e .-2....2...-1....0...-5....0....5....0...-3....5...-5....2....3....5....3....0
%K nonn
%O 1,2
%A _R. H. Hardin_ Aug 02 2011
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