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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
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
1,2
COMMENTS
Sum_{k=A075561(n)..n^2} T(n,k) = A133791(n).
T(n,n^2) = 1.
LINKS
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.
EXAMPLE
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
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).
Sequence in context: A279445 A217285 A212635 * A087108 A021687 A063422
KEYWORD
nonn,tabf,hard
AUTHOR
Eric W. Weisstein, Nov 25 2024
STATUS
approved