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 A346638 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. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The existence of such a six-sided polygon implies that every element of the sextuple is less than the sum of the other elements. LINKS Table of n, a(n) for n=0..29. Giovanni Corbelli, Visual Basic routine for generating number of six-sided polygons Giovanni Corbelli Proof of the formula: Number of k-tuples with elements in {1,2,...,N} corresponding to k-sided polygons Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA 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 PROG (Visual Basic) ' See links. CROSSREFS Cf. A006003, A346636, A346637. Sequence in context: A224137 A016899 A250364 * A017676 A055015 A001014 Adjacent sequences: A346635 A346636 A346637 * A346639 A346640 A346641 KEYWORD nonn,easy AUTHOR Giovanni Corbelli, Jul 26 2021 STATUS approved

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Last modified August 7 11:41 EDT 2024. Contains 375012 sequences. (Running on oeis4.)