This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A378418 #7 Nov 26 2024 09:32:06
%S A378418 1,6,4,1,48,117,126,84,36,9,1,40,560,2736,6800,10310,10560,7832,4352,
%T A378418 1820,560,120,16,1,10,200,3050,31525,188700,677690,1610700,2740775,
%U A378418 3527075,3562700,2895610,1923600,1053175,475950,176600,53105,12650,2300,300,25,1,18
%N 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).
%C A378418 Extended to n=1.
%C A378418 Sum_{k=A094087(n)..n^2} T(n,k) = A303334(n).
%C A378418 T(n,n^2) = 1.
%H A378418 Eric W. Weisstein, <a href="/A378418/b378418.txt">Table of n, a(n) for n = 1..175</a>
%H A378418 Stephan Mertens, <a href="https://arxiv.org/abs/2408.08053">Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph</a>, arXiv:2408.08053 [math.CO], Aug 2024.
%H A378418 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>.
%H A378418 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominationNumber.html">Domination Number</a>.
%H A378418 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominationPolynomial.html">Domination Polynomial</a>.
%H A378418 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TorusGridGraph.html">Torus Grid Graph</a>.
%e A378418 D(1) = x
%e A378418 D(2)= 6*x^2+4*x^3+x^4
%e A378418 D(3) = 48*x^3+117*x^4+126*x^5+84*x^6+36*x^7+9*x^8+x^9
%e A378418 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
%Y A378418 Cf. A094087 (domination number of the n X n torus grid graph).
%Y A378418 Cf. A303334 (number of dominating sets in the n X n torus grid graph).
%Y A378418 Cf. A000290 (vertex count of the n X n torus grid graph = n^2).
%K A378418 nonn,tabf,hard
%O A378418 1,2
%A A378418 _Eric W. Weisstein_, Nov 25 2024