A378412 Irregular triangle read by rows: T(n,k) is the coefficient of x^k in the domination polynomial of the n X n grid graph (n>=1, A104519(n+2)<=k<=n^2).

1, 6, 4, 1, 10, 57, 98, 80, 36, 9, 1, 2, 40, 554, 2484, 5494, 7268, 6402, 3964, 1760, 556, 120, 16, 1, 22, 1545, 22594, 140304, 492506, 1126091, 1823057, 2204694, 2063202, 1528544, 908623, 435832, 168426, 51953, 12550, 2296, 300, 25, 1, 288, 20896, 478624

Offset: 1

Author

Eric W. Weisstein, Nov 25 2024

Keywords

• nonn
• tabf
• hard

Comments

Sum_{k=A104519(n+2)..n^2} T(n,k) = A133515(n).

T(n,n^2) = 1.

Examples

			D_1(x)=x
D_2(x)=6*x^2+4*x^3+x^4
D_3(x)=10*x^3+57*x^4+98*x^5+80*x^6+36*x^7+9*x^8+x^9
D_4(x)=2*x^4+40*x^5+554*x^6+2484*x^7+5494*x^8+7268*x^9+6402*x^10+3964*x^11+1760*x^12+556*x^13+120*x^14+16*x^15+x^16
		

Links

• Eric W. Weisstein, Table of n, a(n) for n = 1..2922
• Stephan Mertens, Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph, arXiv:2408.08053 [math.CO], Aug 2024.
• Eric Weisstein's World of Mathematics, Domatic Number.
• Eric Weisstein's World of Mathematics, Dominating Set.
• Eric Weisstein's World of Mathematics, Domination Number.
• Eric Weisstein's World of Mathematics, Grid Graph.

Crossrefs

Cf. A104519 (domination number of the (n-2) X (n-2) grid graph).

Cf. A133515 (number of dominating sets in the n X n grid graph).

Cf. A000290 (vertex count of the n X n grid graph = n^2).