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 A378412 #8 Nov 26 2024 09:32:11
%S A378412 1,6,4,1,10,57,98,80,36,9,1,2,40,554,2484,5494,7268,6402,3964,1760,
%T A378412 556,120,16,1,22,1545,22594,140304,492506,1126091,1823057,2204694,
%U A378412 2063202,1528544,908623,435832,168426,51953,12550,2296,300,25,1,288,20896,478624
%N A378412 Irregular triangle read by rows: T(n,k) is the coefficient of x^k in the domination polynomial of the n X n grid graph (n>=1, A104519(n+2)<=k<=n^2).
%C A378412 Sum_{k=A104519(n+2)..n^2} T(n,k) = A133515(n).
%C A378412 T(n,n^2) = 1.
%H A378412 Eric W. Weisstein, <a href="/A378412/b378412.txt">Table of n, a(n) for n = 1..2922</a>
%H A378412 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 A378412 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DomaticNumber.html">Domatic Number</a>.
%H A378412 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>.
%H A378412 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominationNumber.html">Domination Number</a>.
%H A378412 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>.
%e A378412 D_1(x)=x
%e A378412 D_2(x)=6*x^2+4*x^3+x^4
%e A378412 D_3(x)=10*x^3+57*x^4+98*x^5+80*x^6+36*x^7+9*x^8+x^9
%e A378412 D_4(x)=2*x^4+40*x^5+554*x^6+2484*x^7+5494*x^8+7268*x^9+6402*x^10+3964*x^11+1760*x^12+556*x^13+120*x^14+16*x^15+x^16
%Y A378412 Cf. A104519 (domination number of the (n-2) X (n-2) grid graph).
%Y A378412 Cf. A133515 (number of dominating sets in the n X n grid graph).
%Y A378412 Cf. A000290 (vertex count of the n X n grid graph = n^2).
%K A378412 nonn,tabf,hard
%O A378412 1,2
%A A378412 _Eric W. Weisstein_, Nov 25 2024