A394659 Number of independent vertex sets of size 7 in the n-triangular grid graph.

0, 0, 0, 0, 27, 6715, 196899, 2547420, 20372485, 118262442, 545477655, 2114805415, 7155153144, 21689622270, 60049653202, 154055280120, 370344275691, 841651316923, 1821128260530, 3773553936582

Offset

1,5

Comments

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

Links

Table of n, a(n) for n=1..20.

Eric Weisstein's World of Mathematics, Independent Vertex Set.

Eric Weisstein's World of Mathematics, Triangular Grid Graph.

Formula

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).

Crossrefs

Cf. A239567 (coefficients of independence polynomial).

Cf. A000012 (number of size 1 sets).

Cf. A239568 (number of size 2 sets).

Cf. A239569 (number of size 3 sets).

Cf. A239570 (number of size 4 sets).

Cf. A239571 (number of size 5 sets).

Cf. A282998 (number of size 6 sets).

Cf. A297557 (number of maximum size sets).

Sequence in context: A123395 A051680 A013828 * A343922 A391640 A209261

Adjacent sequences: A394656 A394657 A394658 * A394660 A394661 A394662

Keyword

nonn,more

Author

Eric W. Weisstein, Mar 27 2026

Status

approved