A378420 Irregular triangle read by rows: T(n,k) is the coefficient of x^k in the domination polynomial of the n X n king graph (n>=1, A075561(n)<=k<=n^2).

1, 4, 6, 4, 1, 1, 10, 48, 106, 122, 84, 36, 9, 1, 256, 1536, 4480, 8320, 10896, 10560, 7744, 4320, 1816, 560, 120, 16, 1, 79, 1593, 14672, 81524, 307244, 842506, 1764068, 2918828, 3909834, 4311034, 3955232, 3038092, 1957940, 1056965, 475304, 176256, 53046, 12646

Offset: 1

Author

Eric W. Weisstein, Nov 25 2024

Keywords

• nonn
• tabf
• hard

Comments

Sum_{k=A075561(n)..n^2} T(n,k) = A133791(n).

T(n,n^2) = 1.

Examples

			D(1)=x
D(2)=4*x+6*x^2+4*x^3+x^4
D(3)=x+10*x^2+48*x^3+106*x^4+122*x^5+84*x^6+36*x^7+9*x^8+x^9
D(4)=256*x^4+1536*x^5+4480*x^6+8320*x^7+10896*x^8+10560*x^9+7744*x^10+4320*x^11+1816*x^12+560*x^13+120*x^14+16*x^15+x^16
		

Links

• Eric W. Weisstein, Table of n, a(n) for n = 1..3333
• 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, Dominating Set.
• Eric Weisstein's World of Mathematics, Domination Number.
• Eric Weisstein's World of Mathematics, Domination Polynomial.
• Eric Weisstein's World of Mathematics, King Graph.

Crossrefs

Cf. A075561 (domination number of the n X n king graph).

Cf. A133791 (number of dominating sets in the n X n king graph).

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