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A182794 Number of n-colorings of the 9 X 9 X 9 triangular grid. 12
0, 0, 0, 6, 67849629696, 17497810918123218900, 21925009706068920874598400, 1045584233565048659578102256250, 6368832392862110714579731514351616, 9534235558912413569697852308677120776 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
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.
LINKS
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).
FORMULA
a(n) = n^45 -108*n^44 + ... (see Maple program).
MAPLE
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);
CROSSREFS
Sequence in context: A058431 A045518 A058457 * A072240 A182795 A182796
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 02 2010
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)