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 A182794 #18 Jan 21 2024 11:56:03 %S A182794 0,0,0,6,67849629696,17497810918123218900,21925009706068920874598400, %T A182794 1045584233565048659578102256250,6368832392862110714579731514351616, %U A182794 9534235558912413569697852308677120776 %N A182794 Number of n-colorings of the 9 X 9 X 9 triangular grid. %C A182794 The 9 X 9 X 9 triangular grid has 9 rows with k vertices in row k. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The graph has 45 vertices and 108 edges altogether. %H A182794 Alois P. Heinz, <a href="/A182794/b182794.txt">Table of n, a(n) for n = 0..1000</a> %H A182794 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic polynomial</a> %H A182794 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lattice_graph#Other_kinds">Triangular grid graph</a> %H A182794 <a href="/index/Rec#order_46">Index entries for linear recurrences with constant coefficients</a>, signature (46, -1035, 15180, -163185, 1370754, -9366819, 53524680, -260932815, 1101716330, -4076350421, 13340783196, -38910617655, 101766230790, -239877544005, 511738760544, -991493848554, 1749695026860, -2818953098830, 4154246671960, -5608233007146, 6943526580276, -7890371113950, 8233430727600, -7890371113950, 6943526580276, -5608233007146, 4154246671960, -2818953098830, 1749695026860, -991493848554, 511738760544, -239877544005, 101766230790, -38910617655, 13340783196, -4076350421, 1101716330, -260932815, 53524680, -9366819, 1370754, -163185, 15180, -1035, 46, -1). %F A182794 a(n) = n^45 -108*n^44 + ... (see Maple program). %p A182794 a:= n-> n^45 -108*n^44 +5714*n^43 -197372*n^42 +5004951*n^41 -99331939*n^40 +1606376002*n^39 -21760175421*n^38+251900492473*n^37 -2529947375509*n^36 +22305591797446*n^35 -174257688976920*n^34 +1215408574487125*n^33 -7615215090082277*n^32 +43080094524111690*n^31 -220967851371444614*n^30 +1031210769134504204*n^29 -4391099235591937845*n^28 +17100876656070073880*n^27 -61022823409833058201*n^26 %p A182794 +199812365243382363912*n^25 -600991376049390898992*n^24 +1661619908871238912196*n^23 -4224371709444972487708*n^22 +9875485316923894342417*n^21 -21221061699176359482887*n^20 +41886723683404956818991*n^19 -75858892195631057087330*n^18 +125862045971633675717554*n^17 -190930468100539717386672*n^16 +264149971345371552591904*n^15 -332242305634477726845448*n^14 +378446023463873654411519*n^13 %p A182794 -388532455150677959308540*n^12 +357418193476328504707252*n^11 -292480744218652691170096*n^10 +210981642121913298294408*n^9 -132621489649268878766112*n^8 +71568787087815309389792*n^7 -32504434438954975091968*n^6 +12087094618713177654080*n^5 -3534893963007018617856*n^4 +762559875649969442816*n^3 -107896190008663345152*n^2 +7511367180771568640*n: seq(a(n), n=0..12); %Y A182794 9th column of A182797. Cf. A178435, A182798, A182788, A182789, A182790, A182791, A182792, A182793, A182795, A182796. %K A182794 nonn,easy %O A182794 0,4 %A A182794 _Alois P. Heinz_, Dec 02 2010