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A346638
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a(n) is the number of 6-tuples (a_1,a_2,a_3,a_4,a_5,a_6) having all terms in {1,...,n} such that there exists a hexagon with these side-lengths.
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3
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0, 1, 64, 729, 4096, 15619, 46614, 117481, 261640, 530181, 997228, 1766017, 2975688, 4808791, 7499506, 11342577, 16702960, 24026185, 33849432, 46813321, 63674416, 85318443, 112774222, 147228313, 190040376, 242759245, 307139716, 385160049, 479040184, 591260671
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OFFSET
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0,3
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COMMENTS
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The existence of such a six-sided polygon implies that every element of the sextuple is less than the sum of the other elements.
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LINKS
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FORMULA
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a(n) = n^6 - 6*binomial(n+1,6) = n^6 - (n+1)*binomial(n,5).
General formula for k-tuples: a_k(n) = n^k - k*binomial(n+1,k) = n^k - (n+1)*binomial(n,k-1).
G.f.: x*(1 + 57*x + 302*x^2 + 302*x^3 + 51*x^4 + x^5)/(1 - x)^7. - Stefano Spezia, Sep 27 2021
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PROG
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(Visual Basic) ' See links.
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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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STATUS
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approved
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