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 A378420 #7 Nov 26 2024 09:31:54
%S A378420 1,4,6,4,1,1,10,48,106,122,84,36,9,1,256,1536,4480,8320,10896,10560,
%T A378420 7744,4320,1816,560,120,16,1,79,1593,14672,81524,307244,842506,
%U A378420 1764068,2918828,3909834,4311034,3955232,3038092,1957940,1056965,475304,176256,53046,12646
%N 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).
%C A378420 Sum_{k=A075561(n)..n^2} T(n,k) = A133791(n).
%C A378420 T(n,n^2) = 1.
%H A378420 Eric W. Weisstein, <a href="/A378420/b378420.txt">Table of n, a(n) for n = 1..3333</a>
%H A378420 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 A378420 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>.
%H A378420 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominationNumber.html">Domination Number</a>.
%H A378420 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominationPolynomial.html">Domination Polynomial</a>.
%H A378420 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingGraph.html">King Graph</a>.
%e A378420 D(1)=x
%e A378420 D(2)=4*x+6*x^2+4*x^3+x^4
%e A378420 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
%e A378420 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
%Y A378420 Cf. A075561 (domination number of the n X n king graph).
%Y A378420 Cf. A133791 (number of dominating sets in the n X n king graph).
%Y A378420 Cf. A000290 (vertex count of the n X n king graph = n^2).
%K A378420 nonn,tabf,hard
%O A378420 1,2
%A A378420 _Eric W. Weisstein_, Nov 25 2024