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 A381726 #19 Mar 22 2025 10:24:35 %S A381726 1,2,1,1,2,13,83,513,4052,41197,462069,5597201,76094134,1153902701, %T A381726 18981358311,336018968449,6413439874792,131386321421901, %U A381726 2867812411156521,66426533670738769,1629082910078009770,42175861619149917325,1148999152027728530363,32856688248674995989889 %N A381726 Number of minimum connected dominating sets in the n X n black bishop graph. %H A381726 Andrew Howroyd, <a href="/A381726/b381726.txt">Table of n, a(n) for n = 1..200</a> %H A381726 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BlackBishopGraph.html">Black Bishop Graph</a>. %H A381726 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedDominatingSet.html">Connected Dominating Set</a>. %F A381726 a(n) = Sum_{k=1..floor((n-1)/2)} A072590(n-2*k, 2*k-1) for n >= 3. - _Andrew Howroyd_, Mar 20 2025 %t A381726 Join[{1, 2}, Table[Sum[(2 k - 1)^(n - 2 k - 1) (n - 2 k)^(2 (k - 1)), {k, Floor[(n - 1)/2]}], {n, 3, 20}]] (* _Eric W. Weisstein_, Mar 22 2025 *) %o A381726 (PARI) \\ B(n,k) is A072590. %o A381726 B(n,k) = n^(k-1) * k^(n-1) %o A381726 a(n) = if(n <= 2, n, sum(k=1, (n-1)\2, B(n-2*k, 2*k-1))) \\ _Andrew Howroyd_, Mar 20 2025 %Y A381726 Cf. A381727 (white bishop). %Y A381726 Cf. A072590, A132609, A289145, A303141, A323500. %K A381726 nonn %O A381726 1,2 %A A381726 _Eric W. Weisstein_, Mar 05 2025 %E A381726 a(10) onwards from _Andrew Howroyd_, Mar 20 2025