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%I #5 Mar 31 2012 12:36:21
%S 1,15,183,953,7799,58661,416291,3109443,22837977,167468295,1233723835,
%T 9067625183,66666846231,490306244985,3605057176121,26508858876345,
%U 194928358871853,1433337703487151,10539668947354103,77500564655649379
%N Number of arrays of -7..7 integers x(1..n) with every x(i) in a subsequence of length 1, 2 or 3 with sum zero
%C Column 7 of A193702
%H R. H. Hardin, <a href="/A193701/b193701.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 9*a(n-1) -20*a(n-2) +37*a(n-3) +15*a(n-4) +1019*a(n-5) -1134*a(n-6) +3436*a(n-7) +33482*a(n-8) +15474*a(n-9) +29711*a(n-10) +961419*a(n-11) +683896*a(n-12) +1825179*a(n-13) +15748458*a(n-14) +23126370*a(n-15) +38173343*a(n-16) +226830379*a(n-17) +370492092*a(n-18) +693250011*a(n-19) +2421116922*a(n-20) +4560273880*a(n-21) +7732685397*a(n-22) +21366673399*a(n-23) +37358020963*a(n-24) +63795649259*a(n-25) +132130836188*a(n-26) +220084075549*a(n-27) +318734402763*a(n-28) +553875929031*a(n-29) +695960384183*a(n-30) +857140665435*a(n-31) +833509394653*a(n-32) +403752920515*a(n-33) -924869997740*a(n-34) -2684878823886*a(n-35) -6810105192532*a(n-36) -8630146012719*a(n-37) -12489403452239*a(n-38) -7743608923054*a(n-39) -1507226640243*a(n-40) +18531908958781*a(n-41) +28906227483030*a(n-42) +50629889861673*a(n-43) +22778866503951*a(n-44) +24323533799816*a(n-45) -59688930677366*a(n-46) -38033966611133*a(n-47) -104749729554957*a(n-48) +399350631980*a(n-49) -21059823178174*a(n-50) +85765269187723*a(n-51) +27966328288586*a(n-52) +57156462274065*a(n-53) -14225844709762*a(n-54) -2982661267389*a(n-55) -28358226843583*a(n-56) -8687424068816*a(n-57) -9542840100107*a(n-58) +1057363759876*a(n-59) +800556394045*a(n-60) +2669712852110*a(n-61) +1420099373699*a(n-62) +1067445742345*a(n-63) +390958931092*a(n-64) +164491015051*a(n-65) +10906818266*a(n-66) -17627332793*a(n-67) -24118310099*a(n-68) -15592708119*a(n-69) -8905368063*a(n-70) -4235152032*a(n-71) -1857411364*a(n-72) -735078659*a(n-73) -268544470*a(n-74) -91160001*a(n-75) -28521516*a(n-76) -8388791*a(n-77) -2244636*a(n-78) -568333*a(n-79) -129069*a(n-80) -27653*a(n-81) -5088*a(n-82) -876*a(n-83) -123*a(n-84) -15*a(n-85) -a(n-86)
%e Some solutions for n=6
%e ..6....0...-6...-5....3....1...-4...-4...-6....5....0....2....2...-6....1....5
%e .-5...-2....4....0....2...-1...-3....0....6...-5...-2...-2....5....2...-7...-4
%e .-1....3....2....5...-5...-4....7....4...-7....3....2....3...-7....4....6...-1
%e .-2...-1...-6...-1...-5....4....0...-1....7...-3...-4...-6....2...-6....7...-2
%e ..3...-7...-6....1....3...-2....5....6....7....1....6....3....4....2...-5....2
%e ..0....7....6...-1....2...-2...-5...-5...-7...-1...-2...-3...-4....0...-2....0
%K nonn
%O 1,2
%A _R. H. Hardin_ Aug 02 2011
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