A378418 Irregular triangle read by rows: T(n,k) is the coefficient of x^k in the domination polynomial of the n X n torus grid graph (n>=1, A094087(n)<=k<=n^2).
1, 6, 4, 1, 48, 117, 126, 84, 36, 9, 1, 40, 560, 2736, 6800, 10310, 10560, 7832, 4352, 1820, 560, 120, 16, 1, 10, 200, 3050, 31525, 188700, 677690, 1610700, 2740775, 3527075, 3562700, 2895610, 1923600, 1053175, 475950, 176600, 53105, 12650, 2300, 300, 25, 1, 18
Offset: 1
Examples
D(1) = x D(2)= 6*x^2+4*x^3+x^4 D(3) = 48*x^3+117*x^4+126*x^5+84*x^6+36*x^7+9*x^8+x^9 D(4) = 40*x^4+560*x^5+2736*x^6+6800*x^7+10310*x^8+10560*x^9+7832*x^10+4352*x^11+1820*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..175
- 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, Torus Grid Graph.
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