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A182794
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Number of n-colorings of the 9 X 9 X 9 triangular grid.
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12
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0, 0, 0, 6, 67849629696, 17497810918123218900, 21925009706068920874598400, 1045584233565048659578102256250, 6368832392862110714579731514351616, 9534235558912413569697852308677120776
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OFFSET
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0,4
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COMMENTS
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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.
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LINKS
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Index entries for linear recurrences with constant coefficients, 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).
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FORMULA
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a(n) = n^45 -108*n^44 + ... (see Maple program).
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MAPLE
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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
+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
-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);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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