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A257934
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Expansion of 1/(1-x-x^2-x^3-x^4+x^5+x^6+x^7).
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0
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1, 1, 2, 4, 8, 14, 26, 48, 89, 163, 300, 552, 1016, 1868, 3436, 6320, 11625, 21381, 39326, 72332, 133040, 244698, 450070, 827808, 1522577, 2800455, 5150840, 9473872, 17425168, 32049880, 58948920, 108423968, 199422769, 366795657, 674642394, 1240860820, 2282298872, 4197802086, 7720961778
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OFFSET
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0,3
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COMMENTS
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This sequence counts partially ordered partitions of (n) into parts (1,2,3,4) in which the position (order) of the 4's are unimportant. For example the permutations of (43421) are counted as permutations of (321)=6.
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LINKS
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FORMULA
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a(n)= a(n-1) + a(n-2) + a(n-3) + a(n-4) - a(n-5) - a(n-6) - a(n-7).
G.f.: 1 / ((x-1)*(x+1)*(x^2+1)*(x^3+x^2+x-1)). - Colin Barker, May 17 2015
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EXAMPLE
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a(6)=26; these are (42=24),(411=141=114),(33),(321=six),(3111=four),(222),(2211=six),(21111=five),(111111).
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PROG
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(PARI) Vec(1 / ((x-1)*(x+1)*(x^2+1)*(x^3+x^2+x-1)) + O(x^100)) \\ Colin Barker, May 17 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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