A394659 - OEIS

%I #11 Mar 31 2026 11:21:15

%S 0,0,0,0,27,6715,196899,2547420,20372485,118262442,545477655,

%T 2114805415,7155153144,21689622270,60049653202,154055280120,

%U 370344275691,841651316923,1821128260530,3773553936582

%N Number of independent vertex sets of size 7 in the n-triangular grid graph.

%C Using the convention that n corresponds to the number of edges on each outer side.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularGridGraph.html">Triangular Grid Graph</a>.

%F For n > 3, a(n) = (n - 4)*(n^13 + 25*n^12 + 9*n^11 - 3555*n^10 - 7745*n^9 + 260563*n^8 + 291075*n^7 - 11898033*n^6 + 10339924*n^5 + 303368632*n^4 - 909281184*n^3 - 2609966352*n^2 + 16737321600*n - 23213352960)/645120 (conjectured).

%Y Cf. A239567 (coefficients of independence polynomial).

%Y Cf. A000012 (number of size 1 sets).

%Y Cf. A239568 (number of size 2 sets).

%Y Cf. A239569 (number of size 3 sets).

%Y Cf. A239570 (number of size 4 sets).

%Y Cf. A239571 (number of size 5 sets).

%Y Cf. A282998 (number of size 6 sets).

%Y Cf. A297557 (number of maximum size sets).

%K nonn,more

%O 1,5

%A _Eric W. Weisstein_, Mar 27 2026