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A368758 Irregular table read by rows: T(n,k) is the number of k-sided regions, k>=3, in the hyperoctahedral (or cocktail party) graph of order n.

%I A368758 #17 Feb 16 2025 08:34:06
%S A368758 0,2,14,2,2,42,22,100,72,12,2,234,142,4,418,320,90,10,734,610,116,44,
%T A368758 1248,878,82,20,14,1968,1454,534,98,12,16,2696,2662,744,74,56,34,4040,
%U A368758 3434,770,74,0,2,5806,4722,1932,430,94,26,7706,7102,2048,894,92,24,10868,7492,1448,406,4
%N A368758 Irregular table read by rows: T(n,k) is the number of k-sided regions, k>=3, in the hyperoctahedral (or cocktail party) graph of order n.
%C A368758 See A368755 and A368756 for further images of the graphs.
%H A368758 Scott R. Shannon, <a href="/A368758/a368758.png">Image for T(8,k)</a>.
%H A368758 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CocktailPartyGraph.html">Cocktail Party Graph</a>.
%F A368758 Sum of row n = A368755(n).
%e A368758 The table begins:
%e A368758 0;
%e A368758 2;
%e A368758 14, 2, 2;
%e A368758 42, 22;
%e A368758 100, 72, 12, 2;
%e A368758 234, 142, 4;
%e A368758 418, 320, 90, 10;
%e A368758 734, 610, 116, 44;
%e A368758 1248, 878, 82, 20, 14;
%e A368758 1968, 1454, 534, 98, 12, 16;
%e A368758 2696, 2662, 744, 74, 56, 34;
%e A368758 4040, 3434, 770, 74, 0, 2;
%e A368758 5806, 4722, 1932, 430, 94, 26;
%e A368758 7706, 7102, 2048, 894, 92, 24;
%e A368758 10868, 7492, 1448, 406, 4;
%e A368758 13438, 12122, 4682, 1356, 206, 4;
%e A368758 17438, 15950, 5420, 2194, 296, 84, 6, 2;
%e A368758 22990, 17734, 7166, 1976, 182, 52;
%e A368758 27284, 25902, 9672, 2718, 772, 182;
%e A368758 34160, 31164, 12650, 3710, 648, 188, 0, 0, 8, 32;
%e A368758 .
%e A368758 .
%Y A368758 Cf. A368755 (regions), A368756 (vertices), A368757 (edges), A129348, A193130, A282010.
%K A368758 nonn,tabf
%O A368758 1,2
%A A368758 _Scott R. Shannon_, Jan 04 2024