cp's OEIS Frontend

A380346 Number of corona for a hexagon of edge n with diamonds of side 1.

%I A380346 #38 May 05 2025 11:44:39
%S A380346 18,198,1298,5778,19602,54758,132498,287298,571538,1060902
%N A380346 Number of corona for a hexagon of edge n with diamonds of side 1.
%C A380346 The number of diamonds that can surround a hexagon(n) fall into four categories: A016945(n), A016945(n) + 1, A016945(n) + 2, and A016945(n) + 3.
%C A380346 The number of coronal tilings for A016945(n) is 2.
%C A380346 The number of coronal tilings for A016945(n) + 1 is 9,36,81,144,225, see A016766.
%C A380346 The number of coronal tilings for A016945(n) + 2 is 6,96,486,1536,3750,7776,14406 = 6*A000583.
%C A380346 The number of coronal tilings for A016945(n) + 3 is 1,64,729,4096,15625, see A001014.
%C A380346 A008793 looks at the enumeration of diamonds inside the hexagon. In contrast this looks at the enumeration of diamond corona of the hexagon.
%H A380346 Craig Knecht, <a href="/A380346/a380346.png">198 diamond corona of the H1 hexagon</a>.
%H A380346 Craig Knecht, <a href="/A380346/a380346_4.png">Coronal corners</a>.
%H A380346 Craig Knecht, <a href="/A380346/a380346_2.png">Example for the sequence</a>.
%H A380346 Craig Knecht, <a href="/A380346/a380346_1.png">H1 corona sorted by the number of coronal tiles</a>.
%H A380346 Craig Knecht, <a href="/A380346/a380346_3.png">Hexagon diamond corona inside a hexagon diamond tiling</a>.
%H A380346 Craig Knecht, Feihu Liu, and Guoce Xin, <a href="https://arxiv.org/abs/2504.19269">Enumeration of Corona for Lozenge Tilings</a>, arXiv:2504.19269 [math.CO], 2025.
%H A380346 Walter Trump, <a href="/A380346/a380346.pdf">Lozenge-Coronae-Around-Hexagon</a>.
%F A380346 a(n) = n^6 + 6*n^5 + 21*n^4 + 44*n^3 + 60*n^2 + 48*n + 18 (conjectured).
%Y A380346 Cf. A001014, A008793, A016766, A016945, A380416.
%K A380346 nonn,more
%O A380346 0,1
%A A380346 _Craig Knecht_, Jan 22 2025