OFFSET
0,3
COMMENTS
The existence of such a five-sided polygon implies that every element of the quintuple is less than the sum of the other elements.
LINKS
Giovanni Corbelli, Visual Basic routine for generating number of five-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 (6,-15,20,-15,6,-1).
FORMULA
a(n) = n^5 - 5*binomial(n+1,5) = n^5 - (n+1)*binomial(n,4).
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 + 26*x + 66*x^2 + 21*x^3 + x^4)/(1 - x)^6. - Stefano Spezia, Sep 27 2021
PROG
(Visual Basic) ' See links.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Giovanni Corbelli, Jul 26 2021
STATUS
approved