

A346636


a(n) is the number of quadruples (a_1, a_2, a_3, a_4) having all terms in {1,...,n} such that there exists a quadrilateral with these side lengths.


3



0, 1, 16, 77, 236, 565, 1156, 2121, 3592, 5721, 8680, 12661, 17876, 24557, 32956, 43345, 56016, 71281, 89472, 110941, 136060, 165221, 198836, 237337, 281176, 330825, 386776, 449541, 519652, 597661, 684140, 779681, 884896, 1000417, 1126896, 1265005, 1415436
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OFFSET

0,3


COMMENTS

The existence of such a foursided polygon implies that every element of the quadruple is less than the sum of the other elements.


LINKS



FORMULA

Formula: a(n) = n^4  4*binomial(n+1,4) = n^4  (n+1)*binomial(n,3).
General formula for ktuples: a_k(n) = n^k  k*binomial(n+1,k) = n^k  (n+1)*binomial(n,k1).


PROG

(Visual Basic) ' See Links.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



