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A193700
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Number of arrays of -6..6 integers x(1..n) with every x(i) in a subsequence of length 1, 2 or 3 with sum zero
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1
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1, 13, 139, 703, 5127, 35121, 231121, 1571745, 10581553, 71181241, 479947725, 3232545773, 21775125291, 146700533417, 988236372613, 6657360614917, 44848171247367, 302123393506887, 2035285492576987, 13710906191405879
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 8*a(n-1) -14*a(n-2) +18*a(n-3) +42*a(n-4) +532*a(n-5) -315*a(n-6) +1840*a(n-7) +12473*a(n-8) +13792*a(n-9) +20549*a(n-10) +255743*a(n-11) +304217*a(n-12) +632955*a(n-13) +2991169*a(n-14) +5389718*a(n-15) +8604964*a(n-16) +30250938*a(n-17) +51494261*a(n-18) +90398324*a(n-19) +208342125*a(n-20) +362582604*a(n-21) +540397472*a(n-22) +1034234494*a(n-23) +1405920463*a(n-24) +1935955787*a(n-25) +2396524190*a(n-26) +2332763945*a(n-27) +808988744*a(n-28) -1439143236*a(n-29) -8362720657*a(n-30) -13069971494*a(n-31) -22093152783*a(n-32) -20609065416*a(n-33) -15506723392*a(n-34) +9043039012*a(n-35) +27240818460*a(n-36) +62586614863*a(n-37) +45043587612*a(n-38) +53875925002*a(n-39) -26366651863*a(n-40) -22697494843*a(n-41) -91636141648*a(n-42) -31865904719*a(n-43) -43383211591*a(n-44) +27951296127*a(n-45) +15841549285*a(n-46) +38065522467*a(n-47) +12105171253*a(n-48) +10539636196*a(n-49) -3371313190*a(n-50) -2950259705*a(n-51) -4982694992*a(n-52) -2717534262*a(n-53) -1854432715*a(n-54) -635721381*a(n-55) -217450973*a(n-56) +38465489*a(n-57) +70279472*a(n-58) +65849635*a(n-59) +39286061*a(n-60) +21034749*a(n-61) +9544870*a(n-62) +3991356*a(n-63) +1490866*a(n-64) +508874*a(n-65) +158820*a(n-66) +45029*a(n-67) +11626*a(n-68) +2618*a(n-69) +535*a(n-70) +92*a(n-71) +13*a(n-72) +a(n-73)
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EXAMPLE
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Some solutions for n=6
..0....3....3....2...-1....3....0...-2...-1....0....6...-1...-1...-6...-3...-6
.-5...-4...-1....1....6....1....0...-3...-3....4...-3....4...-5....6....3....4
..1....1...-2...-3...-5...-4....4....5....4...-2...-3...-3....6....1....4....2
..4...-1...-6....2...-2....3...-3...-5...-4...-2....3....1...-5....2...-4...-5
.-5...-4....5...-4....2...-1...-1....6...-4...-5....0...-2....5...-3....6....2
..0....4....1....4....0...-2....1...-1....4....5....0....1...-5....3...-6....3
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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